1
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Longhi S. Photonic Mpemba effect. OPTICS LETTERS 2024; 49:5188-5191. [PMID: 39270260 DOI: 10.1364/ol.532503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2024] [Accepted: 08/21/2024] [Indexed: 09/15/2024]
Abstract
The Mpemba effect (ME) is the counterintuitive phenomenon in statistical physics for which a far-from-equilibrium state can relax toward equilibrium faster than a state closer to equilibrium. This effect has raised great curiosity for a long time and has been studied extensively in many classical and quantum systems. Here, it is shown that the Mpemba effect can be observed in optics as well. Specifically, the process of light diffusion in finite-sized photonic lattices under incoherent (dephasing) dynamics is considered. Rather surprisingly, it is shown that certain highly localized initial light distributions can diffuse faster than initial broadly delocalized distributions. The effect is illustrated by considering the random walk of optical pulses in fiber-based temporal mesh lattices, which should provide an experimentally accessible setup for the demonstration of the Mpemba effect in optics.
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2
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Joshi LK, Franke J, Rath A, Ares F, Murciano S, Kranzl F, Blatt R, Zoller P, Vermersch B, Calabrese P, Roos CF, Joshi MK. Observing the Quantum Mpemba Effect in Quantum Simulations. PHYSICAL REVIEW LETTERS 2024; 133:010402. [PMID: 39042798 DOI: 10.1103/physrevlett.133.010402] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2024] [Accepted: 03/29/2024] [Indexed: 07/25/2024]
Abstract
The nonequilibrium physics of many-body quantum systems harbors various unconventional phenomena. In this Letter, we experimentally investigate one of the most puzzling of these phenomena-the quantum Mpemba effect, where a tilted ferromagnet restores its symmetry more rapidly when it is farther from the symmetric state compared to when it is closer. We present the first experimental evidence of the occurrence of this effect in a trapped-ion quantum simulator. The symmetry breaking and restoration are monitored through entanglement asymmetry, probed via randomized measurements, and postprocessed using the classical shadows technique. Our findings are further substantiated by measuring the Frobenius distance between the experimental state and the stationary thermal symmetric theoretical state, offering direct evidence of subsystem thermalization.
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Affiliation(s)
- Lata Kh Joshi
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstraße 21a, 6020 Innsbruck, Austria
- University of Innsbruck, Institute for Theoretical Physics, Technikerstraße 21a, 6020 Innsbruck, Austria
- SISSA and INFN, via Bonomea 265, 34136 Trieste, Italy
| | - Johannes Franke
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstraße 21a, 6020 Innsbruck, Austria
- University of Innsbruck, Institute for Experimental Physics, Technikerstraße 25, 6020 Innsbruck, Austria
| | - Aniket Rath
- Univiversité Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France
| | | | - Sara Murciano
- Walter Burke Institute for Theoretical Physics, and Department of Physics and IQIM, Caltech, Pasadena, California 91125, USA
| | - Florian Kranzl
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstraße 21a, 6020 Innsbruck, Austria
- University of Innsbruck, Institute for Experimental Physics, Technikerstraße 25, 6020 Innsbruck, Austria
| | - Rainer Blatt
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstraße 21a, 6020 Innsbruck, Austria
- University of Innsbruck, Institute for Experimental Physics, Technikerstraße 25, 6020 Innsbruck, Austria
| | - Peter Zoller
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstraße 21a, 6020 Innsbruck, Austria
- University of Innsbruck, Institute for Theoretical Physics, Technikerstraße 21a, 6020 Innsbruck, Austria
| | - Benoît Vermersch
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstraße 21a, 6020 Innsbruck, Austria
- University of Innsbruck, Institute for Theoretical Physics, Technikerstraße 21a, 6020 Innsbruck, Austria
- Univiversité Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France
| | - Pasquale Calabrese
- SISSA and INFN, via Bonomea 265, 34136 Trieste, Italy
- International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy
| | - Christian F Roos
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstraße 21a, 6020 Innsbruck, Austria
- University of Innsbruck, Institute for Experimental Physics, Technikerstraße 25, 6020 Innsbruck, Austria
| | - Manoj K Joshi
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstraße 21a, 6020 Innsbruck, Austria
- University of Innsbruck, Institute for Experimental Physics, Technikerstraße 25, 6020 Innsbruck, Austria
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3
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Aharony Shapira S, Shapira Y, Markov J, Teza G, Akerman N, Raz O, Ozeri R. Inverse Mpemba Effect Demonstrated on a Single Trapped Ion Qubit. PHYSICAL REVIEW LETTERS 2024; 133:010403. [PMID: 39042793 DOI: 10.1103/physrevlett.133.010403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2024] [Accepted: 04/24/2024] [Indexed: 07/25/2024]
Abstract
The Mpemba effect is a counterintuitive phenomena in which a hot system reaches a cold temperature faster than a colder system, under otherwise identical conditions. Here, we propose a quantum analog of the Mpemba effect, on the simplest quantum system, a qubit. Specifically, we show it exhibits an inverse effect, in which a cold qubit reaches a hot temperature faster than a hot qubit. Furthermore, in our system a cold qubit can heat up exponentially faster, manifesting the strong version of the effect. This occurs only for sufficiently coherent systems, making this effect quantum mechanical, i.e., due to interference effects. We experimentally demonstrate our findings on a single ^{88}Sr^{+} trapped ion qubit. The existence of this anomalous relaxation effect in simple quantum systems reveals its fundamentality, and may have a role in designing and operating quantum information processing devices.
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Affiliation(s)
- Shahaf Aharony Shapira
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Yotam Shapira
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Jovan Markov
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Gianluca Teza
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Nitzan Akerman
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Oren Raz
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Roee Ozeri
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
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4
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Rylands C, Klobas K, Ares F, Calabrese P, Murciano S, Bertini B. Microscopic Origin of the Quantum Mpemba Effect in Integrable Systems. PHYSICAL REVIEW LETTERS 2024; 133:010401. [PMID: 39042790 DOI: 10.1103/physrevlett.133.010401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2023] [Revised: 03/01/2024] [Accepted: 04/30/2024] [Indexed: 07/25/2024]
Abstract
The highly complicated nature of far from equilibrium systems can lead to a complete breakdown of the physical intuition developed in equilibrium. A famous example of this is the Mpemba effect, which states that nonequilibrium states may relax faster when they are further from equilibrium or, put another way, hot water can freeze faster than warm water. Despite possessing a storied history, the precise criteria and mechanisms underpinning this phenomenon are still not known. Here, we study a quantum version of the Mpemba effect that takes place in closed many-body systems with a U(1) conserved charge: in certain cases a more asymmetric initial configuration relaxes and restores the symmetry faster than a more symmetric one. In contrast to the classical case, we establish the criteria for this to occur in arbitrary integrable quantum systems using the recently introduced entanglement asymmetry. We describe the quantum Mpemba effect in such systems and relate the properties of the initial state, specifically its charge fluctuations, to the criteria for its occurrence. These criteria are expounded using exact analytic and numerical techniques in several examples, a free fermion model, the Rule 54 cellular automaton, and the Lieb-Liniger model.
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Affiliation(s)
- Colin Rylands
- SISSA and INFN Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy
| | - Katja Klobas
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Filiberto Ares
- SISSA and INFN Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy
| | - Pasquale Calabrese
- SISSA and INFN Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy
- International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy
| | - Sara Murciano
- Walter Burke Institute for Theoretical Physics, Caltech, Pasadena, California 91125, USA
- Department of Physics and IQIM, Caltech, Pasadena, California 91125, USA
| | - Bruno Bertini
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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5
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Chatterjee S, Ghosh S, Vadakkayil N, Paul T, Singha SK, Das SK. Mpemba effect in pure spin systems : A universal picture of the role of spatial correlations at initial states. Phys Rev E 2024; 110:L012103. [PMID: 39161011 DOI: 10.1103/physreve.110.l012103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2024] [Accepted: 07/03/2024] [Indexed: 08/21/2024]
Abstract
The quicker freezing of hotter water, than a colder sample, when quenched to a common lower temperature, is referred to as the Mpemba effect (ME). While this counter-intuitive fact remains a surprize since long, efforts have begun to identify similar effect in other systems. We investigate the ME in a rather general context concerning magnetic phase transitions. From Monte Carlo simulations of model systems, viz., the Ising model and the q-state Potts model, with varying range of interaction and space dimension, we assert that hotter paramagnets undergo ferromagnetic ordering faster than the colder ones. This conclusion we have arrived at following the analyses of the simulation results on decay of energy and growth in ordering following quenches from different starting temperatures, to fixed final temperatures below the Curie points. The general observation, in all the considered models, without any element of frustration, is a crucial and important fact of our study. Furthermore, we have obtained an important scaling picture, on the strength of the effect, with respect to the variation in spatial correlation in the initial states. This behavior appears true irrespective of the nature of order-parameter fluctuation and even order of transition. The observations are expected to be relevant to the understanding of ME in a rather general class of systems.
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6
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Rose M, Manikandan SK. Role of interactions in nonequilibrium transformations. Phys Rev E 2024; 109:044136. [PMID: 38755940 DOI: 10.1103/physreve.109.044136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2023] [Accepted: 03/28/2024] [Indexed: 05/18/2024]
Abstract
For arbitrary nonequilibrium transformations in complex systems, we show that the distance between the current state and a target state can be decomposed into two terms: one corresponding to an independent estimate of the distance, and another corresponding to interactions, quantified using the relative mutual information between the variables. This decomposition is a special case of a more general decomposition involving successive orders of correlation or interactions among the degrees of freedom of the system. To illustrate its practical significance, we study the thermal relaxation of two interacting, optically trapped colloidal particles, where increasing pairwise interaction strength is shown to prolong the longevity of the time-dependent nonequilibrium state. Additionally, we study a system with both pairwise and triplet interactions, where our approach identifies their distinct contributions to the transformation. In more general setups where it is possible to control the strength of different orders of interactions, our findings provide a way to disentangle their effects and identify interactions that facilitate the transformation.
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Affiliation(s)
- Maria Rose
- School of Pure and Applied Physics, Mahatma Gandhi University, 686560 Kottayam, India
| | - Sreekanth K Manikandan
- NORDITA, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden and Department of Chemistry, Stanford University, Stanford, California 94305, USA
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7
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Santos A. Mpemba meets Newton: Exploring the Mpemba and Kovacs effects in the time-delayed cooling law. Phys Rev E 2024; 109:044149. [PMID: 38755857 DOI: 10.1103/physreve.109.044149] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2024] [Accepted: 04/01/2024] [Indexed: 05/18/2024]
Abstract
Despite extensive research, the fundamental physical mechanisms underlying the Mpemba effect, a phenomenon where a substance cools faster after initially being heated, remain elusive. Although historically linked with water, the Mpemba effect manifests across diverse systems, sparking heightened interest in Mpemba-like phenomena. Concurrently, the Kovacs effect, a memory phenomenon observed in materials such as polymers, involves rapid quenching and subsequent temperature changes, resulting in nonmonotonic relaxation behavior. This paper probes the intricacies of the Mpemba and Kovacs effects within the framework of the time-delayed Newton's law of cooling, recognized as a simplistic yet effective phenomenological model accommodating memory phenomena. This law allows for a nuanced comprehension of temperature variations, introducing a delay time (τ) and incorporating specific protocols for the thermal bath temperature, contingent on a defined waiting time (t_{w}). Remarkably, the relevant parameter space is two-dimensional (τ and t_{w}), with bath temperatures exerting no influence on the presence or absence of the Mpemba effect or on the relative strength of the Kovacs effect. The findings enhance our understanding of these memory phenomena, providing valuable insights applicable to researchers across diverse fields, ranging from physics to materials science.
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Affiliation(s)
- Andrés Santos
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006 Badajoz, Spain
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8
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Pemartín IGA, Mompó E, Lasanta A, Martín-Mayor V, Salas J. Shortcuts of Freely Relaxing Systems Using Equilibrium Physical Observables. PHYSICAL REVIEW LETTERS 2024; 132:117102. [PMID: 38563945 DOI: 10.1103/physrevlett.132.117102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2023] [Revised: 11/15/2023] [Accepted: 01/18/2024] [Indexed: 04/04/2024]
Abstract
Many systems, when initially placed far from equilibrium, exhibit surprising behavior in their attempt to equilibrate. Striking examples are the Mpemba effect and the cooling-heating asymmetry. These anomalous behaviors can be exploited to shorten the time needed to cool down (or heat up) a system. Though, a strategy to design these effects in mesoscopic systems is missing. We bring forward a description that allows us to formulate such strategies, and, along the way, makes natural these paradoxical behaviors. In particular, we study the evolution of macroscopic physical observables of systems freely relaxing under the influence of one or two instantaneous thermal quenches. The two crucial ingredients in our approach are timescale separation and a nonmonotonic temperature evolution of an important state function. We argue that both are generic features near a first-order transition. Our theory is exemplified with the one-dimensional Ising model in a magnetic field using analytic results and numerical experiments.
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Affiliation(s)
| | - Emanuel Mompó
- Departamento de Matemática Aplicada, Grupo de Dinámica No Lineal, Universidad Pontificia Comillas, Alberto Aguilera 25, 28015 Madrid, Spain
- Instituto de Investigación Tecnológica (IIT), Universidad Pontificia Comillas, 28015 Madrid, Spain
| | - Antonio Lasanta
- Departamento de Álgebra, Facultad de Educación, Economía y Tecnología de Ceuta, Universidad de Granada, Cortadura del Valle, s/n, 51001 Ceuta, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada, Spain
- Nanoparticles Trapping Laboratory, Universidad de Granada, Granada, Spain
| | - Víctor Martín-Mayor
- Departamento de Física Teórica, Universidad Complutense, 28040 Madrid, Spain
- Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50018 Zaragoza, Spain
| | - Jesús Salas
- Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Spain
- Grupo de Teorías de Campos y Física Estadística, Instituto Gregorio Millán, Universidad Carlos III de Madrid, Unidad Asociada al Instituto de Estructura de la Materia, CSIC, Spain
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9
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Chatterjee AK, Takada S, Hayakawa H. Quantum Mpemba Effect in a Quantum Dot with Reservoirs. PHYSICAL REVIEW LETTERS 2023; 131:080402. [PMID: 37683159 DOI: 10.1103/physrevlett.131.080402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2023] [Accepted: 07/17/2023] [Indexed: 09/10/2023]
Abstract
We demonstrate the quantum Mpemba effect in a quantum dot coupled to two reservoirs, described by the Anderson model. We show that the system temperatures starting from two different initial values (hot and cold) cross each other at finite time (and thereby reverse their identities; i.e., hot becomes cold and vice versa) to generate thermal quantum Mpemba effect. The slowest relaxation mode believed to play the dominating role in Mpemba effect in Markovian systems does not contribute to such anomalous relaxation in the present model. In this connection, our analytical result provides necessary condition for producing quantum Mpemba effect in the density matrix elements of the quantum dot, as a combined effect of the remaining relaxation modes.
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Affiliation(s)
- Amit Kumar Chatterjee
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Satoshi Takada
- Department of Mechanical Systems Engineering and Institute of Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Naka-cho, Koganei, Tokyo 184-8588, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan
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10
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Biswas A, Rajesh R. Mpemba effect for a Brownian particle trapped in a single well potential. Phys Rev E 2023; 108:024131. [PMID: 37723739 DOI: 10.1103/physreve.108.024131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Accepted: 08/03/2023] [Indexed: 09/20/2023]
Abstract
The Mpemba effect refers to the counterintuitive phenomenon of a hotter system equilibrating faster than a colder system when both are quenched to the same low temperature. For a Brownian particle trapped in a piecewise linear single well potential that is devoid of any other metastable minima, we show the existence of the Mpemba effect for a wide range of parameters through an exact solution. This result challenges the prevalent explanation of the Mpemba effect that requires the energy landscape to be rugged with multiple minima. We also demonstrate the existence of inverse and strong Mpemba effects.
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Affiliation(s)
- Apurba Biswas
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India and Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - R Rajesh
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India and Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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11
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Biswas A, Prasad VV, Rajesh R. Mpemba effect in driven granular gases: Role of distance measures. Phys Rev E 2023; 108:024902. [PMID: 37723801 DOI: 10.1103/physreve.108.024902] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2023] [Accepted: 07/25/2023] [Indexed: 09/20/2023]
Abstract
The Mpemba effect refers to the counterintuitive effect where a system which is initially further from the final steady state equilibrates faster than an identical system that is initially closer. The closeness to the final state is defined in terms of a distance measure. For driven granular systems, the Mpemba effect has been illustrated in terms of an ad hoc measure of mean kinetic energy as the distance function. In this paper, by studying four different distance measures based on the mean kinetic energies as well as velocity distribution, we show that the Mpemba effect depends on the definition of the measures.
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Affiliation(s)
- Apurba Biswas
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - V V Prasad
- Department of Physics, Cochin University of Science and Technology, Kochi 682022, India
| | - R Rajesh
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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12
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Amorim F, Wisely J, Buckley N, DiNardo C, Sadasivan D. Predicting the Mpemba effect using machine learning. Phys Rev E 2023; 108:024137. [PMID: 37723698 DOI: 10.1103/physreve.108.024137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2022] [Accepted: 08/01/2023] [Indexed: 09/20/2023]
Abstract
The Mpemba effect can be studied with Markovian dynamics in a nonequilibrium thermodynamics framework. The Markovian Mpemba effect can be observed in a variety of systems including the Ising model. We demonstrate that the Markovian Mpemba effect can be predicted in the Ising model with several machine learning methods: the decision tree algorithm, neural networks, linear regression, and nonlinear regression with the least absolute shrinkage and selection operator (LASSO) method. The positive and negative accuracy of these methods are compared. Additionally, we find that machine learning methods can be used to accurately extrapolate to data outside the range in which they were trained. Neural networks can even predict the existence of the Mpemba effect when they are trained only on data in which the Mpemba effect does not occur. This indicates that information about which coefficients result in the Mpemba effect is contained in coefficients where the results does not occur. Furthermore, neural networks can predict that the Mpemba effect does not occur for positive J, corresponding to the ferromagnetic Ising model even when they are only trained on negative J, corresponding to the antiferromagnetic Ising model. All of these results demonstrate that the Mpemba effect can be predicted in complex, computationally expensive systems, without explicit calculations of the eigenvectors.
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Affiliation(s)
| | - Joey Wisely
- Ave Maria University, Ave Maria, Florida 34142, USA
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13
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Biswas A, Rajesh R, Pal A. Mpemba effect in a Langevin system: Population statistics, metastability, and other exact results. J Chem Phys 2023; 159:044120. [PMID: 37522403 DOI: 10.1063/5.0155855] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2023] [Accepted: 07/06/2023] [Indexed: 08/01/2023] Open
Abstract
The Mpemba effect is a fingerprint of the anomalous relaxation phenomenon wherein an initially hotter system equilibrates faster than an initially colder system when both are quenched to the same low temperature. Experiments on a single colloidal particle trapped in a carefully shaped double well potential have demonstrated this effect recently [A. Kumar and J. Bechhoefer, Nature 584, 64 (2020)]. In a similar vein, here, we consider a piece-wise linear double well potential that allows us to demonstrate the Mpemba effect using an exact analysis based on the spectral decomposition of the corresponding Fokker-Planck equation. We elucidate the role of the metastable states in the energy landscape as well as the initial population statistics of the particles in showcasing the Mpemba effect. Crucially, our findings indicate that neither the metastability nor the asymmetry in the potential is a necessary or a sufficient condition for the Mpemba effect to be observed.
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Affiliation(s)
- Apurba Biswas
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - R Rajesh
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Arnab Pal
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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14
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Das SK. Perspectives on a Few Puzzles in Phase Transformations: When Should the Farthest Reach the Earliest? LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2023. [PMID: 37499235 DOI: 10.1021/acs.langmuir.3c00668] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/29/2023]
Abstract
We briefly review the facts concerning two important aspects of phase transitions, namely, critical and coarsening phenomena. A discussion of the universal features, highlighting the current challenges, is provided. Following this, we elaborate on a topic of much recent interest, viz., the Mpemba effect, a puzzle that found mention even in the works of Aristotle. After a description of the debated case of faster freezing of a hotter sample of liquid water, into ice, than a colder one, when quenched to the same subzero temperature, we discuss more modern interest. There one asks, should a hotter body of a material equilibrate faster than a colder one when quenched to a common lower temperature? Within this broad scenario, we focus on magnetic systems. A surprising observation of the effect during the para- to ferromagnetic transition, in a simple model system, viz., the nearest-neighbor Ising model, without any built-in frustration, is described. Some associated future directions are pointed out. A discussion is provided by considering the effect as a kinetic outcome in the background of critical phenomena. A picture is drawn by putting emphasis on the role of spatial correlations in the initial configurations alongside discussing the importance of frustration and metastability in evolution from one state to another. In connection with dynamical freezing, concerning metastability, we have introduced the complex Ginzburg-Landau equation that has relevance in phase transitions, chemical oscillations, and elsewhere. For this model and a few other cases also, we have described how a lack of order or correlation in certain parameters can lead to quicker evolution.
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Affiliation(s)
- Subir K Das
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
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15
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Teza G, Yaacoby R, Raz O. Relaxation Shortcuts through Boundary Coupling. PHYSICAL REVIEW LETTERS 2023; 131:017101. [PMID: 37478423 DOI: 10.1103/physrevlett.131.017101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2021] [Revised: 07/06/2022] [Accepted: 05/17/2023] [Indexed: 07/23/2023]
Abstract
When a hot system cools down faster than an equivalent cold one, it exhibits the Mpemba effect (ME). This counterintuitive phenomenon was observed in several systems including water, magnetic alloys, and polymers. In most experiments the system is coupled to the bath through its boundaries, but all theories so far assumed bulk coupling. Here we build a general framework to characterize anomalous relaxations through boundary coupling, and present two emblematic setups: a diffusing particle and an Ising antiferromagnet. In the latter, we show that the ME can survive even arbitrarily weak couplings.
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Affiliation(s)
- Gianluca Teza
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Ran Yaacoby
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Oren Raz
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
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16
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Ivander F, Anto-Sztrikacs N, Segal D. Hyperacceleration of quantum thermalization dynamics by bypassing long-lived coherences: An analytical treatment. Phys Rev E 2023; 108:014130. [PMID: 37583187 DOI: 10.1103/physreve.108.014130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Accepted: 06/28/2023] [Indexed: 08/17/2023]
Abstract
We develop a perturbative technique for solving Markovian quantum dissipative dynamics, with the perturbation parameter being a small gap in the eigenspectrum. As an example, we apply the technique and straightforwardly obtain analytically the dynamics of a three-level system with quasidegenerate excited states, where quantum coherences persist for very long times, proportional to the inverse of the energy splitting squared. We then show how to bypass this long-lived coherent dynamics and accelerate the relaxation to thermal equilibration in a hyper-exponential manner, a Markovian quantum-assisted Mpemba-like effect. This hyperacceleration of the equilibration process manifests if the initial state is carefully prepared, such that its coherences precisely store the amount of population relaxing from the initial condition to the equilibrium state. Our analytical method for solving quantum dissipative dynamics readily provides equilibration timescales, and as such it reveals how coherent and incoherent effects interlace in the dynamics. It further advises on how to accelerate relaxation processes, which is desirable when long-lived quantum coherences stagnate dynamics.
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Affiliation(s)
- Felix Ivander
- Chemical Physics Theory Group, Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George Street, Toronto, Ontario, Canada M5S 3H6
| | - Nicholas Anto-Sztrikacs
- Department of Physics, 60 Saint George Street, University of Toronto, Toronto, Ontario, Canada M5S 1A7
| | - Dvira Segal
- Chemical Physics Theory Group, Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George Street, Toronto, Ontario, Canada M5S 3H6
- Department of Physics, 60 Saint George Street, University of Toronto, Toronto, Ontario, Canada M5S 1A7
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17
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Weber M, Freericks JK. Electronic Mechanism that Quenches Field-Driven Heating as Illustrated with the Static Holstein Model. PHYSICAL REVIEW LETTERS 2023; 130:266401. [PMID: 37450792 DOI: 10.1103/physrevlett.130.266401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2021] [Accepted: 06/01/2023] [Indexed: 07/18/2023]
Abstract
Time-dependent driving of quantum systems has emerged as a powerful tool to engineer exotic phases far from thermal equilibrium, but in the presence of many-body interactions it also leads to runaway heating, so that generic systems are believed to heat up until they reach a featureless infinite-temperature state. Understanding the mechanisms by which such a heat death can be slowed down or even avoided is a major goal-one such mechanism is to drive toward an even distribution of electrons in momentum space. Here we show how such a mechanism avoids runaway heating for an interacting charge-density-wave chain with a macroscopic number of conserved quantities when driven by a strong dc electric field; minibands with nontrivial distribution functions develop as the current is prematurely driven to zero. Moreover, when approaching a zero-temperature resonance, the field strength can tune between positive, negative, or close-to-infinite effective temperatures for each miniband. Our results suggest that nontrivial metastable distribution functions should be realized in the prethermal regime of quantum systems coupled to slow bosonic modes.
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Affiliation(s)
- Manuel Weber
- Department of Physics, Georgetown University, Washington, D.C. 20057, USA
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, 01187 Dresden, Germany
- Institut für Theoretische Physik and Würzburg-Dresden Cluster of Excellence ct.qmat, Technische Universität Dresden, 01062 Dresden, Germany
| | - James K Freericks
- Department of Physics, Georgetown University, Washington, D.C. 20057, USA
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18
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Teza G, Yaacoby R, Raz O. Eigenvalue Crossing as a Phase Transition in Relaxation Dynamics. PHYSICAL REVIEW LETTERS 2023; 130:207103. [PMID: 37267560 DOI: 10.1103/physrevlett.130.207103] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Accepted: 04/07/2023] [Indexed: 06/04/2023]
Abstract
When a system's parameter is abruptly changed, a relaxation toward the new equilibrium of the system follows. We show that a crossing between the second and third eigenvalues of the relaxation operator results in a singularity in the dynamics analogous to a first-order equilibrium phase transition. While dynamical phase transitions are intrinsically hard to detect in nature, here we show how this kind of transition can be observed in an experimentally feasible four-state colloidal system. Finally, analytical proof of survival in the thermodynamic limit of a many body (1D Ising) model is provided.
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Affiliation(s)
- Gianluca Teza
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Ran Yaacoby
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Oren Raz
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
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19
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Liu J, Li J, Liu B, Hamley IW, Jiang S. Mpemba effect in crystallization of polybutene-1. SOFT MATTER 2023; 19:3337-3347. [PMID: 37096363 DOI: 10.1039/d3sm00309d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
The Mpemba effect and its inverse can be understood as a result of nonequilibrium thermodynamics. In polymers, changes of state are generally non-equilibrium processes. However, the Mpemba effect has been rarely reported in the crystallization of polymers. In the melt, polybutene-1 (PB-1) has the lowest critical cooling rate in polyolefins and tends to maintain its original structure and properties with thermal history. A nascent PB-1 sample was prepared by using metallocene catalysis at low temperature, and the crystallization behavior and crystalline structure of the PB-1 were characterized by DSC and WAXS. Experimentally, a clear Mpemba effect is observed not only in the crystallization of the nascent PB-1 melt in form II but also in form I obtained from the nascent PB-1 at low melting temperature. It is proposed that this is due to the differences in the chain conformational entropy in the lattice which influence conformational relaxation times. The entropy and the relaxation time can be predicted using the Adam-Gibbs equations, whereas non-equilibrium thermodynamics is required to describe the crystallization with the Mpemba effect.
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Affiliation(s)
- Jinghua Liu
- School of Materials Science and Engineering, Tianjin University, Tianjin, 300072, China.
| | - Jingqing Li
- School of Materials Science and Engineering, Tianjin University, Tianjin, 300072, China.
| | - Binyuan Liu
- Hebei Key Laboratory of Functional Polymer Materials, School of Chemical Engineering and Science, Hebei University of Technology, Tianjin 300130, China
| | - Ian W Hamley
- School of Chemistry, Pharmacy and Food Biosciences, University of Reading, Whiteknights, Reading RG6 6AD, UK
| | - Shichun Jiang
- School of Materials Science and Engineering, Tianjin University, Tianjin, 300072, China.
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20
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Cao Z, Bao R, Zheng J, Hou Z. Fast Functionalization with High Performance in the Autonomous Information Engine. J Phys Chem Lett 2023; 14:66-72. [PMID: 36566388 DOI: 10.1021/acs.jpclett.2c03335] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Mandal and Jarzynski have proposed a fully autonomous information heat engine, consisting of a demon, a mass, and a memory register interacting with a thermal reservoir. This device converts thermal energy into mechanical work by writing information to a memory register or, conversely, erasing information by consuming mechanical work. Here, we derive a speed limit inequality between the relaxation time of state transformation and the distance between the initial and final distributions, where the combination of the dynamical activity and entropy production plays an important role. Such inequality provides a hint that a speed-performance trade-off relation exists between the relaxation time to a functional state and the average production. To obtain fast functionalization while maintaining the performance, we show that the relaxation dynamics of the information heat engine can be accelerated significantly by devising an optimal initial state of the demon. Our design principle is inspired by the so-called Mpemba effect, where water freezes faster when initially heated.
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Affiliation(s)
- Zhiyu Cao
- Department of Chemical Physics and Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui230026, China
| | - Ruicheng Bao
- Department of Chemical Physics and Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui230026, China
| | - Jiming Zheng
- Department of Chemical Physics and Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui230026, China
| | - Zhonghuai Hou
- Department of Chemical Physics and Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui230026, China
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21
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Dey R, Kundu A, Das B, Banerjee A. Experimental verification of arcsine laws in mesoscopic nonequilibrium systems. Phys Rev E 2022; 106:054113. [PMID: 36559344 DOI: 10.1103/physreve.106.054113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2022] [Accepted: 10/04/2022] [Indexed: 06/17/2023]
Abstract
A large number of processes in the mesoscopic world occur out of equilibrium, where the time evolution of a system becomes immensely important since it is driven principally by dissipative effects. Nonequilibrium steady states (NESS) represent a crucial category in such systems, where relaxation timescales are comparable to the operational timescales. In this study, we employ a model NESS stochastic system, which is comprised of a colloidal microparticle optically trapped in a viscous fluid, externally driven by a temporally correlated noise, and show that time-integrated observables such as the entropic current, the work done on the system or the work dissipated by it, follow the three Lévy arcsine laws [A. C. Barato et al., Phys. Rev. Lett. 121, 090601 (2018)0031-900710.1103/PhysRevLett.121.090601], in the large time limit. We discover that cumulative distributions converge faster to arcsine distributions when it is near equilibrium and the rate of entropy production is small, because in that case the entropic current has weaker temporal autocorrelation. We study this phenomenon by changing the strength of the added noise as well as by perturbing our system with a flow field produced by a microbubble at close proximity to the trapped particle. We confirm our experimental findings with theoretical simulations of the systems. Our work provides an interesting insight into the NESS statistics of the meso-regime, where stochastic fluctuations play a pivotal role.
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Affiliation(s)
- Raunak Dey
- Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur Campus, Mohanpur, West Bengal 741246, India and School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Avijit Kundu
- Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur Campus, Mohanpur, West Bengal 741246, India
| | - Biswajit Das
- Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur Campus, Mohanpur, West Bengal 741246, India
| | - Ayan Banerjee
- Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur Campus, Mohanpur, West Bengal 741246, India
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22
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Megías A, Santos A. Kinetic Theory and Memory Effects of Homogeneous Inelastic Granular Gases under Nonlinear Drag. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1436. [PMID: 37420455 PMCID: PMC9601354 DOI: 10.3390/e24101436] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2022] [Revised: 10/03/2022] [Accepted: 10/04/2022] [Indexed: 06/18/2023]
Abstract
We study a dilute granular gas immersed in a thermal bath made of smaller particles with masses not much smaller than the granular ones in this work. Granular particles are assumed to have inelastic and hard interactions, losing energy in collisions as accounted by a constant coefficient of normal restitution. The interaction with the thermal bath is modeled by a nonlinear drag force plus a white-noise stochastic force. The kinetic theory for this system is described by an Enskog-Fokker-Planck equation for the one-particle velocity distribution function. To get explicit results of the temperature aging and steady states, Maxwellian and first Sonine approximations are developed. The latter takes into account the coupling of the excess kurtosis with the temperature. Theoretical predictions are compared with direct simulation Monte Carlo and event-driven molecular dynamics simulations. While good results for the granular temperature are obtained from the Maxwellian approximation, a much better agreement, especially as inelasticity and drag nonlinearity increase, is found when using the first Sonine approximation. The latter approximation is, additionally, crucial to account for memory effects such as Mpemba and Kovacs-like ones.
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Affiliation(s)
- Alberto Megías
- Departamento de Física, Universidad de Extremadura, E-06006 Badajoz, Spain
| | - Andrés Santos
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006 Badajoz, Spain
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23
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Schwarzendahl FJ, Löwen H. Anomalous Cooling and Overcooling of Active Colloids. PHYSICAL REVIEW LETTERS 2022; 129:138002. [PMID: 36206411 DOI: 10.1103/physrevlett.129.138002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2021] [Revised: 07/14/2022] [Accepted: 08/10/2022] [Indexed: 06/16/2023]
Abstract
The phenomenon that a system at a hot temperature cools faster than at a warm temperature, referred to as the Mpemba effect, has recently been realized for trapped colloids. Here, we investigate the cooling and heating process of a self-propelled active colloid using numerical simulations and theoretical calculations with a model that can be directly tested in experiments. Upon cooling, activity induces a Mpemba effect and the active particle transiently escapes an effective temperature description. At the end of the cooling process the notion of temperature is recovered and the system can exhibit even smaller temperatures than its final temperature, a surprising phenomenon which we refer to as activity-induced overcooling.
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Affiliation(s)
- Fabian Jan Schwarzendahl
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
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24
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Zhang S, Hou JX. Theoretical model for the Mpemba effect through the canonical first-order phase transition. Phys Rev E 2022; 106:034131. [PMID: 36266910 DOI: 10.1103/physreve.106.034131] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2022] [Accepted: 09/09/2022] [Indexed: 06/16/2023]
Abstract
The Mpemba effect is the phenomenon in which the system with high initial temperature cools faster than the system with low initial temperature when all other conditions are the same. A theoretical model of the Mpemba effect through the canonical first-order phase transition is proposed in this paper, which shows that in the cooling processes, the path of the first-order phase transition of the system with the high initial temperature does not pass through any metastable state, while the path of the first-order phase transition of the system with the low initial temperature passes through a metastable state, which leads to the occurrence of the Mpemba effect. Then an example of the theoretical model is given in the Blume-Emery-Griffiths model. The Monte Carlo algorithm is adopted to calculate the estimated times for both systems with different initial temperature to cool down and undergo a first-order phase transition. The simulation results demonstrate a Mpemba effect in the system. Moreover, the evolution paths of the first-order phase transitions of the systems with high and low initial temperatures are given, respectively. The theoretical model presented here may help explain the Mpemba effect in water.
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Affiliation(s)
- Sheng Zhang
- School of Physics, Southeast University, Nanjing 211189, China
| | - Ji-Xuan Hou
- School of Physics, Southeast University, Nanjing 211189, China
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25
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Wang J. Mpemba effect - the effect of time. SCIENCEOPEN RESEARCH 2022. [DOI: 10.14293/s2199-1006.1.sor.2022.0001.v1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022] Open
Abstract
By analyzing the relation between time and speed, the relation between time and gravitational field, the gravitational redshift of photon and the black-body radiation theorem, the conclusion that time on an object is proportional to the fourth power of the absolute temperature of the object is obtained. Applying the above conclusion about the nature of time, the author analyzes the Mpemba effect and the inverse Mpemba effect, and reaches the following conclusion: the Mpemba effect is the time effect produced when heat flows from objects into space, and the “inverse” Mpemba effect is the time effect produced when heat flows from space into objects.
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Affiliation(s)
- Jian’an Wang
- Department of Physics, Shenzhen University, Shenzhen, China
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26
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Megías A, Santos A, Prados A. Thermal versus entropic Mpemba effect in molecular gases with nonlinear drag. Phys Rev E 2022; 105:054140. [PMID: 35706208 DOI: 10.1103/physreve.105.054140] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2022] [Accepted: 05/09/2022] [Indexed: 06/15/2023]
Abstract
Loosely speaking, the Mpemba effect appears when hotter systems cool sooner or, in a more abstract way, when systems further from equilibrium relax faster. In this paper, we investigate the Mpemba effect in a molecular gas with nonlinear drag, both analytically (by employing the tools of kinetic theory) and numerically (direct simulation Monte Carlo of the kinetic equation and event-driven molecular dynamics). The analysis is carried out via two alternative routes, recently considered in the literature: first, the kinetic or thermal route, in which the Mpemba effect is characterized by the crossing of the evolution curves of the kinetic temperature (average kinetic energy), and, second, the stochastic thermodynamics or entropic route, in which the Mpemba effect is characterized by the crossing of the distance to equilibrium in probability space. In general, a nonmutual correspondence between the thermal and entropic Mpemba effects is found, i.e., there may appear the thermal effect without its entropic counterpart or vice versa. Furthermore, a nontrivial overshoot with respect to equilibrium of the thermal relaxation makes it necessary to revise the usual definition of the thermal Mpemba effect, which is shown to be better described in terms of the relaxation of the local equilibrium distribution. Our theoretical framework, which involves an extended Sonine approximation in which not only the excess kurtosis but also the sixth cumulant is retained, gives an excellent account of the behavior observed in simulations.
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Affiliation(s)
- Alberto Megías
- Departamento de Física, Universidad de Extremadura, E-06006 Badajoz, Spain
| | - Andrés Santos
- Departamento de Física, Universidad de Extremadura, E-06006 Badajoz, Spain and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006 Badajoz, Spain
| | - Antonio Prados
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain
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27
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Żuk PJ, Makuch K, Hołyst R, Maciołek A. Transient dynamics in the outflow of energy from a system in a nonequilibrium stationary state. Phys Rev E 2022; 105:054133. [PMID: 35706157 DOI: 10.1103/physreve.105.054133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2022] [Accepted: 03/30/2022] [Indexed: 06/15/2023]
Abstract
We investigate the thermal relaxation of an ideal gas from a nonequilibrium stationary state. The gas is enclosed between two walls, which initially have different temperatures. After making one of the walls adiabatic, the system returns to equilibrium. We notice two distinct modes of heat transport and associated timescales: one connected with a traveling heat front and the other with internal energy diffusion. At the heat front, which moves at the speed of sound, pressure, temperature, and density change abruptly, leaving lower values behind. This is unlike a shock wave, a sound wave, or a thermal wave. The front moves multiple times between the walls and is the dominant heat transport mode until surpassed by diffusion. We found that it can constitute an order 1 factor in shaping the dynamics of the outflow of internal energy. We found that cooling such a system is quicker than heating, and that hotter bodies cool down quicker than colder ones. The latter is known as the Mpemba effect.
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Affiliation(s)
- Paweł J Żuk
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, PL-01-224 Warsaw, Poland
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - Karol Makuch
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, PL-01-224 Warsaw, Poland
| | - Robert Hołyst
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, PL-01-224 Warsaw, Poland
| | - Anna Maciołek
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, PL-01-224 Warsaw, Poland
- Max-Planck-Institut für Intelligente Systeme Stuttgart, Heisenbergstrasse 3, D-70569 Stuttgart, Germany
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28
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Schwarcz D, Burov S. Self-assembly of two-dimensional, amorphous materials on a liquid substrate. Phys Rev E 2022; 105:L022601. [PMID: 35291111 DOI: 10.1103/physreve.105.l022601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2021] [Accepted: 01/26/2022] [Indexed: 06/14/2023]
Abstract
Recent experimental utilization of liquid substrate in the production of two-dimensional crystals, such as graphene, together with a general interest in amorphous materials, raises the following question: is it beneficial to use a liquid substrate to optimize amorphous material production? Inspired by epitaxial growth, we use a two-dimensional coarse-grained model of interacting particles to show that introducing a motion for the substrate atoms improves the self-assembly process of particles that move on top of the substrate. We find that a specific amount of substrate liquidity (for a given sample temperature) is needed to achieve optimal self-assembly. Our results illustrate the opportunities that the combination of different degrees of freedom provides to the self-assembly processes.
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Affiliation(s)
- Deborah Schwarcz
- Physics Department, Bar-Ilan University, Ramat Gan 5290002, Israel
| | - Stanislav Burov
- Physics Department, Bar-Ilan University, Ramat Gan 5290002, Israel
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29
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Kumar A, Chétrite R, Bechhoefer J. Anomalous heating in a colloidal system. Proc Natl Acad Sci U S A 2022; 119:e2118484119. [PMID: 35078935 PMCID: PMC8812517 DOI: 10.1073/pnas.2118484119] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2021] [Accepted: 12/20/2021] [Indexed: 11/18/2022] Open
Abstract
We report anomalous heating in a colloidal system, an experimental observation of the inverse Mpemba effect, where for two initial temperatures lower than the temperature of the thermal bath, the colder of the two systems heats up faster when coupled to the same thermal bath. For an overdamped, Brownian colloidal particle moving in a tilted double-well potential, we find a nonmonotonic dependence of the heating times on the initial temperature of the system. Entropic effects make the inverse Mpemba effect generically weaker-harder to observe-than the usual Mpemba effect (anomalous cooling). We also observe a strong version of anomalous heating, where a cold system heats up exponentially faster than systems prepared under slightly different conditions.
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Affiliation(s)
- Avinash Kumar
- Department of Physics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada
| | - Raphaël Chétrite
- Laboratoire J. A. Dieudonné, UMR CNRS 7351, Université de Nice Sophia Antipolis, 06108 Nice, France
| | - John Bechhoefer
- Department of Physics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada;
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30
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Ruiz-Pino N, Prados A. Optimal Control of Uniformly Heated Granular Fluids in Linear Response. ENTROPY (BASEL, SWITZERLAND) 2022; 24:131. [PMID: 35052157 PMCID: PMC8774495 DOI: 10.3390/e24010131] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/15/2021] [Revised: 01/04/2022] [Accepted: 01/12/2022] [Indexed: 02/01/2023]
Abstract
We present a detailed analytical investigation of the optimal control of uniformly heated granular gases in the linear regime. The intensity of the stochastic driving is therefore assumed to be bounded between two values that are close, which limits the possible values of the granular temperature to a correspondingly small interval. Specifically, we are interested in minimising the connection time between the non-equilibrium steady states (NESSs) for two different values of the granular temperature by controlling the time dependence of the driving intensity. The closeness of the initial and target NESSs make it possible to linearise the evolution equations and rigorously-from a mathematical point of view-prove that the optimal controls are of bang-bang type, with only one switching in the first Sonine approximation. We also look into the dependence of the optimal connection time on the bounds of the driving intensity. Moreover, the limits of validity of the linear regime are investigated.
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Affiliation(s)
| | - Antonio Prados
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain;
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31
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Patrón A, Sánchez-Rey B, Prados A. Strong nonexponential relaxation and memory effects in a fluid with nonlinear drag. Phys Rev E 2022; 104:064127. [PMID: 35030916 DOI: 10.1103/physreve.104.064127] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2021] [Accepted: 11/24/2021] [Indexed: 11/07/2022]
Abstract
We analyze the dynamical evolution of a fluid with nonlinear drag, for which binary collisions are elastic, described at the kinetic level by the Enskog-Fokker-Planck equation. This model system, rooted in the theory of nonlinear Brownian motion, displays a really complex behavior when quenched to low temperatures. Its glassy response is controlled by a long-lived nonequilibrium state, independent of the degree of nonlinearity and also of the Brownian-Brownian collisions rate. The latter property entails that this behavior persists in the collisionless case, where the fluid is described by the nonlinear Fokker-Planck equation. The observed response, which includes nonexponential, algebraic, relaxation, and strong memory effects, presents scaling properties: the time evolution of the temperature-for both relaxation and memory effects-falls onto a master curve, regardless of the details of the experiment. To account for the observed behavior in simulations, it is necessary to develop an extended Sonine approximation for the kinetic equation-which considers not only the fourth cumulant but also the sixth one.
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Affiliation(s)
- A Patrón
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain
| | - B Sánchez-Rey
- Departamento de Física Aplicada I, E.P.S., Universidad de Sevilla, Virgen de África 7, E-41011 Sevilla, Spain
| | - A Prados
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain
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32
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Lin J, Li K, He J, Ren J, Wang J. Power statistics of Otto heat engines with the Mpemba effect. Phys Rev E 2022; 105:014104. [PMID: 35193214 DOI: 10.1103/physreve.105.014104] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2021] [Accepted: 12/14/2021] [Indexed: 01/13/2023]
Abstract
The Mpemba effect is a counterintuitive relaxation phenomenon whereby a system with a higher initial temperature may cool down to the thermal state faster than an identical system that was initially prepared at a lower temperature. Here, we investigate heat and work in a Markovian state transition system with cyclic switching hot-cold temperatures, which operates as an Otto heat engine working in long but finite time, either with or without the Mpemba effect. Under the condition of the periodic steady state having been reached, the time durations of the heating and cooling relaxation processes are determined by exploring a distance-from-equilibrium equivalent to the Kullback-Leibler divergence. We then numerically evaluate and compare the averages and variances of both the work and the power output of two scenarios with and without the Mpemba effect. The results show that the Markovian Mpemba effect can enhance the machine performance by significantly increasing the power output for a given efficiency without sacrificing the stability.
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Affiliation(s)
- Jie Lin
- Department of Physics, Nanchang University, Nanchang 330031, China
| | - Kai Li
- Department of Physics, Nanchang University, Nanchang 330031, China
| | - Jizhou He
- Department of Physics, Nanchang University, Nanchang 330031, China
| | - Jie Ren
- Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Sciences and Engineering, Tongji University, Shanghai 200092, China
| | - Jianhui Wang
- Department of Physics, Nanchang University, Nanchang 330031, China.,State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
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33
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Yang ZY, Hou JX. Mpemba effect of a mean-field system: The phase transition time. Phys Rev E 2022; 105:014119. [PMID: 35193204 DOI: 10.1103/physreve.105.014119] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2021] [Accepted: 01/06/2022] [Indexed: 06/14/2023]
Abstract
The counterintuitive phenomenon-that an initially hotter water freezes faster than initially cooler water-is named the "Mpemba effect." Although it has been known for centuries, the underlying mechanism remains unclear. Recently, the Mpemba effect rekindled the interest of researchers since several studies identified that it might occur in some Markovian systems, and a general statistical-physical Mpemba effect framework was correspondingly proposed. In our previous study [Z.-Y. Yang and J.-X. Hou, Phys. Rev. E 101, 052106 (2020)10.1103/PhysRevE.101.052106], we observed the non-Markovian Mpemba effect in a mean-field system (MFS), where the Mpemba effect originates from the back-reaction of the thermal reservoir. Naturally, the phase transition time is the key to the occurrence of the Mpemba effect, which, however, has not been quantitatively described. Following the direction of previous work, this study rigorously derives the phase transition time under different conditions, and quantitatively describes the mechanism of the non-Markovian Mpemba effect in a MFS. In addition, the validation of our theory was further verified via the microcanonical Monte Carlo simulation. An accurate description of the underlying mechanism of our proposed MFS facilitates the generalization of the Mpemba effect framework in statistical physics and may benefit in answering the riddle of the century, the original Mpemba effect in water.
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Affiliation(s)
- Zhen-Yu Yang
- School of Physics, Southeast University, Nanjing 211189, China
| | - Ji-Xuan Hou
- School of Physics, Southeast University, Nanjing 211189, China
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34
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González-Adalid Pemartín I, Mompó E, Lasanta A, Martín-Mayor V, Salas J. Slow growth of magnetic domains helps fast evolution routes for out-of-equilibrium dynamics. Phys Rev E 2021; 104:044114. [PMID: 34781476 DOI: 10.1103/physreve.104.044114] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2021] [Accepted: 09/21/2021] [Indexed: 11/07/2022]
Abstract
Cooling and heating faster a system is a crucial problem in science, technology, and industry. Indeed, choosing the best thermal protocol to reach a desired temperature or energy is not a trivial task. Noticeably, we find that the phase transitions may speed up thermalization in systems where there are no conserved quantities. In particular, we show that the slow growth of magnetic domains shortens the overall time that the system takes to reach a final desired state. To prove that statement, we use intensive numerical simulations of a prototypical many-body system, namely, the two-dimensional Ising model.
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Affiliation(s)
| | - Emanuel Mompó
- Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Spain
| | - Antonio Lasanta
- Departamento de Álgebra, Facultad de Educación, Economía y Tecnología de Ceuta, Universidad de Granada, Cortadura del Valle, s/n, 51001 Ceuta, Spain.,Grupo de Teorías de Campos y Física Estadística, Instituto Gregorio Millán, Universidad Carlos III de Madrid, Unidad Asociada al Instituto de Estructura de la Materia, CSIC, Spain
| | - Víctor Martín-Mayor
- Departamento de Física Teórica, Universidad Complutense, 28040 Madrid, Spain.,Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50018 Zaragoza, Spain
| | - Jesús Salas
- Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Spain.,Grupo de Teorías de Campos y Física Estadística, Instituto Gregorio Millán, Universidad Carlos III de Madrid, Unidad Asociada al Instituto de Estructura de la Materia, CSIC, Spain
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35
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Critical dynamics and phase transition of a strongly interacting warm spin gas. Proc Natl Acad Sci U S A 2021; 118:2106400118. [PMID: 34686598 DOI: 10.1073/pnas.2106400118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 09/17/2021] [Indexed: 11/18/2022] Open
Abstract
Phase transitions are emergent phenomena where microscopic interactions drive a disordered system into a collectively ordered phase. Near the boundary between two phases, the system can exhibit critical, scale-invariant behavior. Here, we report on a second-order phase transition accompanied by critical behavior in a system of warm cesium spins driven by linearly polarized light. The ordered phase exhibits macroscopic magnetization when the interactions between the spins become dominant. We measure the phase diagram of the system and observe the collective behavior near the phase boundaries, including power-law dependence of the magnetization and divergence of the susceptibility. Out of equilibrium, we observe a critical slowdown of the spin response time by two orders of magnitude, exceeding 5 s near the phase boundary. This work establishes a controlled platform for investigating equilibrium and nonequilibrium properties of magnetic phases.
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36
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Meibohm J, Forastiere D, Adeleke-Larodo T, Proesmans K. Relaxation-speed crossover in anharmonic potentials. Phys Rev E 2021; 104:L032105. [PMID: 34654171 DOI: 10.1103/physreve.104.l032105] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2021] [Accepted: 09/08/2021] [Indexed: 11/07/2022]
Abstract
In a recent Letter [A. Lapolla and A. Godec, Phys. Rev. Lett. 125, 110602 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.110602], thermal relaxation was observed to occur faster from cold to hot (heating) than from hot to cold (cooling). Here we show that overdamped diffusion in anharmonic potentials generically exhibits both faster heating and faster cooling, depending on the initial temperatures and on the potential's degree of anharmonicity. We draw a relaxation-speed phase diagram that localizes the different behaviors in parameter space. In addition to faster-heating and faster-cooling regions, we identify a crossover region in the phase diagram, where heating is initially slower but asymptotically faster than cooling. The structure of the phase diagram is robust against the inclusion of a confining, harmonic term in the potential as well as moderate changes of the measure used to define initially equidistant temperatures.
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Affiliation(s)
- Jan Meibohm
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Danilo Forastiere
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Tunrayo Adeleke-Larodo
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Karel Proesmans
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg.,Hasselt University, B-3590 Diepenbeek, Belgium
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37
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Militaru A, Lasanta A, Frimmer M, Bonilla LL, Novotny L, Rica RA. Kovacs Memory Effect with an Optically Levitated Nanoparticle. PHYSICAL REVIEW LETTERS 2021; 127:130603. [PMID: 34623831 DOI: 10.1103/physrevlett.127.130603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2021] [Accepted: 08/12/2021] [Indexed: 06/13/2023]
Abstract
The understanding of the dynamics of nonequilibrium cooling and heating processes at the nanoscale is still an open problem. These processes can follow surprising relaxation paths due to, e.g., memory effects, which significantly alter the expected equilibration routes. The Kovacs effect can take place when a thermalization process is suddenly interrupted by a change of the bath temperature, leading to a nonmonotonic evolution of the energy of the system. Here, we demonstrate that the Kovacs effect can be observed in the thermalization of the center of mass motion of a levitated nanoparticle. The temperature is controlled during the experiment through an external source of white Gaussian noise that mimics an effective thermal bath at a temperature that can be changed faster than any relaxation time of the system. We describe our experiments in terms of the dynamics of a Brownian particle in a harmonic trap without any fitting parameter, suggesting that the Kovacs effect can appear in a large variety of systems.
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Affiliation(s)
- Andrei Militaru
- Photonics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Antonio Lasanta
- Departamento de Álgebra, Facultad de Educación, Economía y Tecnología de Ceuta, Universidad de Granada, Cortadura del Valle, s/n, 51001 Ceuta, Spain
- Grupo de Teorías de Campos y Física Estadística, Instituto Gregorio Millán, Universidad Carlos III de Madrid, Unidad Asociada al Instituto de Estructura de la Materia, CSIC, Spain
- Grupo de Matemática Aplicada a la Física de la Materia Condensada, Instituto Gregorio Millán, Universidad Carlos III de Madrid, Unidad Asociada al Instituto de Ciencias de Materiales de Madrid, CSIC, Spain
- Nanoparticles Trapping Laboratory, Universidad de Granada, 18071 Granada, Spain
| | - Martin Frimmer
- Photonics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Luis L Bonilla
- Grupo de Matemática Aplicada a la Física de la Materia Condensada, Instituto Gregorio Millán, Universidad Carlos III de Madrid, Unidad Asociada al Instituto de Ciencias de Materiales de Madrid, CSIC, Spain
- Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Spain
- Instituto Gregorio Millán, Universidad Carlos III de Madrid, 28911 Leganés, Spain
| | - Lukas Novotny
- Photonics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Raúl A Rica
- Nanoparticles Trapping Laboratory, Universidad de Granada, 18071 Granada, Spain
- Universidad de Granada, Department of Applied Physics and Research Unit "Modeling Nature" (MNat), 18071 Granada, Spain
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38
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Carollo F, Lasanta A, Lesanovsky I. Exponentially Accelerated Approach to Stationarity in Markovian Open Quantum Systems through the Mpemba Effect. PHYSICAL REVIEW LETTERS 2021; 127:060401. [PMID: 34420328 DOI: 10.1103/physrevlett.127.060401] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2021] [Accepted: 07/02/2021] [Indexed: 06/13/2023]
Abstract
Ergodicity breaking and slow relaxation are intriguing aspects of nonequilibrium dynamics both in classical and quantum settings. These phenomena are typically associated with phase transitions, e.g., the emergence of metastable regimes near a first-order transition or scaling dynamics in the vicinity of critical points. Despite being of fundamental interest the associated divergent timescales are a hindrance when trying to explore steady-state properties. Here we show that the relaxation dynamics of Markovian open quantum systems can be accelerated exponentially by devising an optimal unitary transformation that is applied to the quantum system immediately before the actual dynamics. This initial "rotation" is engineered in such a way that the state of the quantum system no longer excites the slowest decaying dynamical mode. We illustrate our idea-which is inspired by the so-called Mpemba effect, i.e., water freezing faster when initially heated up-by showing how to achieve an exponential speeding-up in the convergence to stationarity in Dicke models, and how to avoid metastable regimes in an all-to-all interacting spin system.
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Affiliation(s)
- Federico Carollo
- Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Antonio Lasanta
- Departamento de Álgebra, Facultad de Educación, Economía y Tecnología de Ceuta, Universidad de Granada, E-51001 Ceuta, Spain
- G. Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
| | - Igor Lesanovsky
- Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
- School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, The University of Nottingham, Nottingham NG7 2RD, United Kingdom
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39
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Sanders S, Zundel L, Kort-Kamp WJM, Dalvit DAR, Manjavacas A. Near-Field Radiative Heat Transfer Eigenmodes. PHYSICAL REVIEW LETTERS 2021; 126:193601. [PMID: 34047587 DOI: 10.1103/physrevlett.126.193601] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2021] [Accepted: 04/12/2021] [Indexed: 06/12/2023]
Abstract
The near-field electromagnetic interaction between nanoscale objects produces enhanced radiative heat transfer that can greatly surpass the limits established by far-field blackbody radiation. Here, we present a theoretical framework to describe the temporal dynamics of the radiative heat transfer in ensembles of nanostructures, which is based on the use of an eigenmode expansion of the equations that govern this process. Using this formalism, we identify the fundamental principles that determine the thermalization of collections of nanostructures, revealing general but often unintuitive dynamics. Our results provide an elegant and precise approach to efficiently analyze the temporal dynamics of the near-field radiative heat transfer in systems containing a large number of nanoparticles.
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Affiliation(s)
- Stephen Sanders
- Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87106, USA
| | - Lauren Zundel
- Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87106, USA
| | - Wilton J M Kort-Kamp
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Diego A R Dalvit
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Alejandro Manjavacas
- Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87106, USA
- Instituto de Óptica (IO-CSIC), Consejo Superior de Investigaciones Científicas, 28006 Madrid, Spain
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40
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Tournier RF, Ojovan MI. Building and Breaking Bonds by Homogenous Nucleation in Glass-Forming Melts Leading to Transitions in Three Liquid States. MATERIALS 2021; 14:ma14092287. [PMID: 33925086 PMCID: PMC8124720 DOI: 10.3390/ma14092287] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/26/2021] [Revised: 04/21/2021] [Accepted: 04/26/2021] [Indexed: 12/11/2022]
Abstract
The thermal history of melts leads to three liquid states above the melting temperatures Tm containing clusters-bound colloids with two opposite values of enthalpy +Δεlg × ΔHm and -Δεlg × ΔHm and zero. All colloid bonds disconnect at Tn+ > Tm and give rise in congruent materials, through a first-order transition at TLL = Tn+, forming a homogeneous liquid, containing tiny superatoms, built by short-range order. In non-congruent materials, (Tn+) and (TLL) are separated, Tn+ being the temperature of a second order and TLL the temperature of a first-order phase transition. (Tn+) and (TLL) are predicted from the knowledge of solidus and liquidus temperatures using non-classical homogenous nucleation. The first-order transition at TLL gives rise by cooling to a new liquid state containing colloids. Each colloid is a superatom, melted by homogeneous disintegration of nuclei instead of surface melting, and with a Gibbs free energy equal to that of a liquid droplet containing the same magic atom number. Internal and external bond number of colloids increases at Tn+ or from Tn+ to Tg. These liquid enthalpies reveal the natural presence of colloid-colloid bonding and antibonding in glass-forming melts. The Mpemba effect and its inverse exist in all melts and is due to the presence of these three liquid states.
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Affiliation(s)
- Robert F. Tournier
- LNCMI-EMFL, CNRS, Université Grenoble Alpes, INSA-T, UPS, 38042 Grenoble, France
- Correspondence:
| | - Michael I. Ojovan
- Department of Materials, Imperial College London, London SW7 2AZ, UK;
- Department of Radiochemistry, Lomonosov Moscow State University, 119991 Moscow, Russia
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41
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Takada S, Hayakawa H, Santos A. Mpemba effect in inertial suspensions. Phys Rev E 2021; 103:032901. [PMID: 33862769 DOI: 10.1103/physreve.103.032901] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2020] [Accepted: 02/10/2021] [Indexed: 11/07/2022]
Abstract
The Mpemba effect (a counterintuitive thermal relaxation process where an initially hotter system may cool down to the steady state sooner than an initially colder system) is studied in terms of a model of inertial suspensions under shear. The relaxation to a common steady state of a suspension initially prepared in a quasiequilibrium state is compared with that of a suspension initially prepared in a nonequilibrium sheared state. Two classes of Mpemba effect are identified, the normal and the anomalous one. The former is generic, in the sense that the kinetic temperature starting from a cold nonequilibrium sheared state is overtaken by the one starting from a hot quasiequilibrium state, due to the absence of initial viscous heating in the latter, resulting in a faster initial cooling. The anomalous Mpemba effect is opposite to the normal one since, despite the initial slower cooling of the nonequilibrium sheared state, it can eventually overtake an initially colder quasiequilibrium state. The theoretical results based on kinetic theory agree with those obtained from event-driven simulations for inelastic hard spheres. It is also confirmed the existence of the inverse Mpemba effect, which is a peculiar heating process, in these suspensions. More particularly, we find the existence of a mixed process in which both heating and cooling can be observed during relaxation.
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Affiliation(s)
- Satoshi Takada
- Institute of Engineering, Tokyo University of Agriculture and Technology, 2-24-16, Naka-cho, Koganei, Tokyo 184-8588, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Andrés Santos
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06071 Badajoz, Spain
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42
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Tozzi A. Why Should Natural Principles Be Simple? PHILOSOPHIA (RAMAT-GAN, ISRAEL) 2021; 50:321-335. [PMID: 33879931 PMCID: PMC8051000 DOI: 10.1007/s11406-021-00359-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/06/2021] [Accepted: 03/10/2021] [Indexed: 06/12/2023]
Abstract
One of the criteria to a strong principle in natural sciences is simplicity. The conventional view holds that the world is provided with natural laws that must be simple. This common-sense approach is a modern rewording of the medieval philosophical/theological concept of the Multiple arising from (and generated by) the One. Humans need to pursue unifying frameworks, classificatory criteria and theories of everything. Still, the fact that our cognitive abilities tend towards simplification and groupings does not necessarily entail that this is the way the world works. Here we ask: what if singularity does not pave the way to multiplicity? How will we be sure if the Ockham's razor holds in real life? We will show in the sequel that the propensity to reduce to simplicity the relationships among the events leads to misleading interpretations of scientific issues. We are not going to take a full sceptic turn: we will engage in active outreach, suggesting examples from biology and physics to demonstrate how a novel methodological antiunitary approach might help to improve our scientific attitude towards world affairs. We will provide examples from aggregation of SARS-Cov-2 particles, unclassified extinct creatures, pathological brain stiffness. Further, we will describe how antiunitary strategies, plagiarising medieval concepts from William od Ockham and Gregory of Rimini, help to explain novel relational approaches to quantum mechanics and the epistemological role of our mind in building the real world.
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Affiliation(s)
- Arturo Tozzi
- Center for Nonlinear Science, Department of Physics, University of North Texas, 1155 Union Circle, #311427, Denton, TX 76203-5017 USA
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43
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Li G, Tu ZC. Equilibrium free-energy differences from a linear nonequilibrium equality. Phys Rev E 2021; 103:032146. [PMID: 33862756 DOI: 10.1103/physreve.103.032146] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2020] [Accepted: 03/04/2021] [Indexed: 11/07/2022]
Abstract
Extracting equilibrium information from nonequilibrium measurements is a challenge task of great importance in understanding the thermodynamic properties of physical, chemical, and biological systems. The discovery of the Jarzynski equality illumines the way to estimate the equilibrium free-energy difference from the work performed in nonequilibrium driving processes. However, the nonlinear (exponential) relation causes the poor convergence of the Jarzynski equality. Here, we propose a concise method to estimate the free-energy difference through a linear nonequilibrium equality which inherently converges faster than nonlinear nonequilibrium equalities. This linear nonequilibrium equality relies on an accelerated isothermal process which is realized by using a unified variational approach, named variational shortcuts to isothermality. We apply our method to an underdamped Brownian particle moving in a double-well potential. The simulations confirm that the method can be used to accurately estimate the free-energy difference with high efficiency. Especially during fast driving processes with high dissipation, the method can improve the accuracy by more than an order of magnitude compared with the estimator based on the nonlinear nonequilibrium equality.
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Affiliation(s)
- Geng Li
- CAS Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.,Graduate School of China Academy of Engineering Physics, Beijing 100193, China
| | - Z C Tu
- Department of Physics, Beijing Normal University, Beijing 100875, China
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44
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Vadakkayil N, Das SK. Should a hotter paramagnet transform quicker to a ferromagnet? Monte Carlo simulation results for Ising model. Phys Chem Chem Phys 2021; 23:11186-11190. [PMID: 33949508 DOI: 10.1039/d1cp00879j] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
For quicker formation of ice, before inserting inside a refrigerator, heating up of a body of water can be beneficial. We report first observation of a counterpart of this intriguing fact, referred to as the Mpemba effect (ME), during ordering in ferromagnets. By performing Monte Carlo simulations of a generic model, we have obtained results on relaxation of systems that are quenched to sub-critical state points from various temperatures above the critical point. For a fixed final temperature, a system with higher starting temperature equilibrates faster than the one prepared at a lower temperature, implying the presence of ME. The observation is extremely counter-intuitive, particularly because of the fact that the model has no in-built frustration or metastability that typically is thought to provide ME. Via the calculations of nonequilibrium properties concerning structure and energy, we quantify the role of critical fluctuations behind this fundamental as well as technologically relevant observation.
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Affiliation(s)
- Nalina Vadakkayil
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India.
| | - Subir K Das
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India.
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45
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Lapolla A, Godec A. Faster Uphill Relaxation in Thermodynamically Equidistant Temperature Quenches. PHYSICAL REVIEW LETTERS 2020; 125:110602. [PMID: 32975999 DOI: 10.1103/physrevlett.125.110602] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2020] [Revised: 06/13/2020] [Accepted: 08/10/2020] [Indexed: 05/29/2023]
Abstract
We uncover an unforeseen asymmetry in relaxation: for a pair of thermodynamically equidistant temperature quenches, one from a lower and the other from a higher temperature, the relaxation at the ambient temperature is faster in the case of the former. We demonstrate this finding on hand of two exactly solvable many-body systems relevant in the context of single-molecule and tracer-particle dynamics. We prove that near stable minima and for all quadratic energy landscapes it is a general phenomenon that also exists in a class of non-Markovian observables probed in single-molecule and particle-tracking experiments. The asymmetry is a general feature of reversible overdamped diffusive systems with smooth single-well potentials and occurs in multiwell landscapes when quenches disturb predominantly intrawell equilibria. Our findings may be relevant for the optimization of stochastic heat engines.
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Affiliation(s)
- Alessio Lapolla
- Mathematical bioPhysics group, Max Planck Institute for Biophysical Chemistry, Göttingen 37077, Germany
| | - Aljaž Godec
- Mathematical bioPhysics group, Max Planck Institute for Biophysical Chemistry, Göttingen 37077, Germany
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46
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Burridge HC, Hallstadius O. Observing the Mpemba effect with minimal bias and the value of the Mpemba effect to scientific outreach and engagement. Proc Math Phys Eng Sci 2020. [DOI: 10.1098/rspa.2019.0829] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The Mpemba effect is the assertion that it is quicker to cool or freeze water when the initial temperature is high. We define the Mpemba effect to have been observed when two samples of water, one initially warmer than the other, are cooled and the initially hotter sample freezes or cools to a prescribed temperature in less time; this assumes that the samples are of the same mass, are at least as pure as drinking water, the cooling is delivered to both samples in the same manner and the same level of insulation is applied to both. Under this definition, we enable repeatable observations of the Mpemba effect by systematically introducing increased nucleation sites (in our case by roughening the container walls with sandpaper) within the cooling environment of the initially warmer sample. We remain able to observe the Mpemba effect when the enthalpy of cooling and freezing the initially warmer sample exceeds that of the initially cooler sample by over 50%, corresponding to a difference in the initial temperatures of around 50 °C. The context of this study, initiated by a high-school student who then carried out all of the experiments, highlights the value of the Mpemba effect as a tool for scientific learning and engagement.
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Affiliation(s)
- Henry C. Burridge
- Department of Civil and Environmental Engineering, Imperial College London, Skempton Building, South Kensington Campus, London SW7 2AZ, UK
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47
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Exponentially faster cooling in a colloidal system. Nature 2020; 584:64-68. [DOI: 10.1038/s41586-020-2560-x] [Citation(s) in RCA: 40] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2020] [Accepted: 05/15/2020] [Indexed: 11/08/2022]
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Biswas A, Prasad VV, Raz O, Rajesh R. Mpemba effect in driven granular Maxwell gases. Phys Rev E 2020; 102:012906. [PMID: 32794966 DOI: 10.1103/physreve.102.012906] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2020] [Accepted: 07/02/2020] [Indexed: 06/11/2023]
Abstract
A Mpemba effect refers to the counterintuitive result that, when quenched to a low temperature, a system at higher temperature may equilibrate faster than one at intermediate temperatures. This effect has recently been demonstrated in driven granular gases, both for smooth as well as rough hard-sphere systems based on a perturbative analysis. In this paper, we consider the inelastic driven Maxwell gas, a simplified model for a granular gas, where the rate of collision is assumed to be independent of the relative velocity. Through an exact analysis, we determine the conditions under which the Mpemba effect is present in this model. For monodispersed gases, we show that the Mpemba effect is present only when the initial states are allowed to be nonstationary, while for bidispersed gases, it is present for some steady-state initial states. We also demonstrate the existence of the strong Mpemba effect for bidispersed Maxwell gas, wherein the system at higher temperature relaxes to a final steady state at an exponentially faster rate leading to smaller equilibration time.
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Affiliation(s)
- Apurba Biswas
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - V V Prasad
- Department of Physics of Complex Systems, Weizmann Institute of Science, 76100 Rehovot, Israel
- Government Arts and Science College, Nadapuram, Kozhikode 673506, India
| | - O Raz
- Department of Physics of Complex Systems, Weizmann Institute of Science, 76100 Rehovot, Israel
| | - R Rajesh
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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Yang ZY, Hou JX. Non-Markovian Mpemba effect in mean-field systems. Phys Rev E 2020; 101:052106. [PMID: 32575203 DOI: 10.1103/physreve.101.052106] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2019] [Accepted: 04/15/2020] [Indexed: 11/07/2022]
Abstract
Under certain conditions, a counterintuitive behavior-an initially hotter sample freezes faster when quenched to a cold bath than an identical system initialled at a lower temperature-is known as the Mpemba effect (ME). Here we identify the existence of the ME in mean-field systems (MFS). Specifically, the thermal contact between MFS and a large thermal reservoir is built up using the microcanonical Monte Carlo algorithm. The simulation results unambiguously demonstrate that an initial hotter system undergoes the paramagnetic-ferromagnetic phase transition faster than the initial cooler one. The ME here originates from the back-reaction of the MFS system on the reservoir, which is thus an embodiment of non-Markovianness in relaxation. In addition, we confirm that the ME survives in the thermodynamic limit. And the significance of reservoir size is also explored: A smaller heat reservoir facilitates the overall relaxation process. In general, this work establishes a theoretical non-Markovian ME framework, which may shed light on widening the understanding of the mechanism behind the ME in other substances, including water.
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Affiliation(s)
- Zhen-Yu Yang
- School of Physics, Southeast University, Nanjing 211189, China
| | - Ji-Xuan Hou
- School of Physics, Southeast University, Nanjing 211189, China
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Gal A, Raz O. Precooling Strategy Allows Exponentially Faster Heating. PHYSICAL REVIEW LETTERS 2020; 124:060602. [PMID: 32109080 DOI: 10.1103/physrevlett.124.060602] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2019] [Revised: 11/26/2019] [Accepted: 01/22/2020] [Indexed: 06/10/2023]
Abstract
What is the fastest way to heat a system which is coupled to a temperature controlled oven? The intuitive answer is to use only the hottest temperature available. However, we show that often it is possible to achieve an exponentially faster heating protocol. Surprisingly, this protocol can have a precooling stage-cooling the system before heating it shortens the heating time significantly. To demonstrate such improvements in many-body systems, we developed a projection-based method with which such protocols can be found in large systems, as we demonstrate on the 2D antiferromagnet Ising model.
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Affiliation(s)
- A Gal
- Department of Physics of Complex Systems, Weizmann Institute of Science, 76100 Rehovot, Israel
| | - O Raz
- Department of Physics of Complex Systems, Weizmann Institute of Science, 76100 Rehovot, Israel
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