1
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Kumar V, Pal A, Shpielberg O. Arrhenius law for interacting diffusive systems. Phys Rev E 2024; 109:L032101. [PMID: 38632768 DOI: 10.1103/physreve.109.l032101] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2023] [Accepted: 02/08/2024] [Indexed: 04/19/2024]
Abstract
Finding the mean time it takes for a particle to escape from a metastable state due to thermal fluctuations is a fundamental problem in physics, chemistry, and biology. Here, we consider the escape rate of interacting diffusive particles, from a deep potential trap within the framework of the macroscopic fluctuation theory-a nonequilibrium hydrodynamic theory. For systems without excluded volume, our investigation reveals adherence to the well-established Arrhenius law. However, in the presence of excluded volume, a universality class emerges, fundamentally altering the escape rate. Remarkably, the modified escape rate within this universality class is independent of the interactions at play. The universality class, demonstrating the importance of excluded volume effects, may bring insights to the interpretation of escape processes in the realm of chemical physics.
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Affiliation(s)
- Vishwajeet Kumar
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Arnab Pal
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Ohad Shpielberg
- Department of Mathematics and Physics, University of Haifa at Oranim, Kiryat Tivon 3600600, Israel
- Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, Abba Khoushy Avenue 199, Haifa 3498838, Israel
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2
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Gutiérrez R, Pérez-Espigares C. Dynamical phase transition to localized states in the two-dimensional random walk conditioned on partial currents. Phys Rev E 2021; 104:044134. [PMID: 34781446 DOI: 10.1103/physreve.104.044134] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2021] [Accepted: 10/12/2021] [Indexed: 11/07/2022]
Abstract
The study of dynamical large deviations allows for a characterization of stationary states of lattice gas models out of equilibrium conditioned on averages of dynamical observables. The application of this framework to the two-dimensional random walk conditioned on partial currents reveals the existence of a dynamical phase transition between delocalized band dynamics and localized vortex dynamics. We present a numerical microscopic characterization of the phases involved and provide analytical insight based on the macroscopic fluctuation theory. A spectral analysis of the microscopic generator shows that the continuous phase transition is accompanied by spontaneous Z_{2}-symmetry breaking whereby the stationary solution loses the reflection symmetry of the generator. Dynamical phase transitions similar to this one, which do not rely on exclusion effects or interactions, are likely to be observed in more complex nonequilibrium physics models.
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Affiliation(s)
- Ricardo Gutiérrez
- Complex Systems Interdisciplinary Group (GISC), Department of Mathematics, Universidad Carlos III de Madrid, Leganés 28911, Madrid, Spain
| | - Carlos Pérez-Espigares
- Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, Granada 18071, Spain.,Institute Carlos I for Theoretical and Computational Physics, Universidad de Granada, Granada 18071, Spain
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3
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Casert C, Vieijra T, Whitelam S, Tamblyn I. Dynamical Large Deviations of Two-Dimensional Kinetically Constrained Models Using a Neural-Network State Ansatz. PHYSICAL REVIEW LETTERS 2021; 127:120602. [PMID: 34597112 DOI: 10.1103/physrevlett.127.120602] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2020] [Revised: 07/13/2021] [Accepted: 07/28/2021] [Indexed: 06/13/2023]
Abstract
We use a neural-network ansatz originally designed for the variational optimization of quantum systems to study dynamical large deviations in classical ones. We use recurrent neural networks to describe the large deviations of the dynamical activity of model glasses, kinetically constrained models in two dimensions. We present the first finite size-scaling analysis of the large-deviation functions of the two-dimensional Fredrickson-Andersen model, and explore the spatial structure of the high-activity sector of the South-or-East model. These results provide a new route to the study of dynamical large-deviation functions, and highlight the broad applicability of the neural-network state ansatz across domains in physics.
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Affiliation(s)
- Corneel Casert
- Department of Physics and Astronomy, Ghent University, 9000 Ghent, Belgium
| | - Tom Vieijra
- Department of Physics and Astronomy, Ghent University, 9000 Ghent, Belgium
| | - Stephen Whitelam
- Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA
| | - Isaac Tamblyn
- Department of Physics, University of Ottawa, K1N 6N5, Ontario, Canada
- Vector Institute for Artificial Intelligence, Toronto, M5G 1M1, Ontario, Canada
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4
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Marcantoni S, Pérez-Espigares C, Garrahan JP. Symmetry-induced fluctuation relations for dynamical observables irrespective of their behavior under time reversal. Phys Rev E 2020; 101:062142. [PMID: 32688517 DOI: 10.1103/physreve.101.062142] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2020] [Accepted: 06/05/2020] [Indexed: 11/07/2022]
Abstract
We extend previous work to describe a class of fluctuation relations (FRs) that emerge as a consequence of symmetries at the level of stochastic trajectories in Markov chains. We prove that given such a symmetry, and for a suitable dynamical observable, it is always possible to obtain a FR under a biased dynamics corresponding to the so-called generalized Doob transform. The general transformations of the dynamics that we consider go beyond time-reversal or spatial isometries, and an implication is the existence of FRs for observables irrespective of their behavior under time reversal, for example for time-symmetric observables rather than currents. We further show how to deduce in the long-time limit these FRs from the symmetry properties of the generator of the dynamics. We illustrate our results with four examples that highlight the novel features of our work.
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Affiliation(s)
- Stefano Marcantoni
- School of Physics & 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
| | - Carlos Pérez-Espigares
- Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, Granada 18071, Spain.,Institute Carlos I for Theoretical and Computational Physics, Universidad de Granada, Granada 18071, Spain
| | - Juan P Garrahan
- School of Physics & 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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Pérez-Espigares C, Hurtado PI. Sampling rare events across dynamical phase transitions. CHAOS (WOODBURY, N.Y.) 2019; 29:083106. [PMID: 31472495 DOI: 10.1063/1.5091669] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2019] [Accepted: 07/16/2019] [Indexed: 06/10/2023]
Abstract
Interacting particle systems with many degrees of freedom may undergo phase transitions to sustain atypical fluctuations of dynamical observables such as the current or the activity. In some cases, this leads to symmetry-broken space-time trajectories which enhance the probability of such events due to the emergence of ordered structures. Despite their conceptual and practical importance, these dynamical phase transitions (DPTs) at the trajectory level are difficult to characterize due to the low probability of their occurrence. However, during the last decade, advanced computational techniques have been developed to measure rare events in simulations of many-particle systems that allow the direct observation and characterization of these DPTs. Here we review the application of a particular rare-event simulation technique, based on cloning Monte Carlo methods, to characterize DPTs in paradigmatic stochastic lattice gases. In particular, we describe in detail some tricks and tips of the trade, paying special attention to the measurement of order parameters capturing the physics of the different DPTs, as well as to the finite-size effects (both in the system size and in the number of clones) that affect the measurements. Overall, we provide a consistent picture of the phenomenology associated with DPTs and their measurement.
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Affiliation(s)
- Carlos Pérez-Espigares
- Departamento de Electromagnetismo y Física de la Materia, and Institute Carlos I for Theoretical and Computational Physics, Universidad de Granada, Granada 18071, Spain
| | - Pablo I Hurtado
- Departamento de Electromagnetismo y Física de la Materia, and Institute Carlos I for Theoretical and Computational Physics, Universidad de Granada, Granada 18071, Spain
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6
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Garrido PL, Hurtado PI, Tizón-Escamilla N. Infinite family of universal profiles for heat current statistics in Fourier's law. Phys Rev E 2019; 99:022134. [PMID: 30934242 DOI: 10.1103/physreve.99.022134] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2018] [Indexed: 06/09/2023]
Abstract
Using tools from large deviation theory, we study fluctuations of the heat current in a model of d-dimensional incompressible fluid driven out of equilibrium by a temperature gradient. We find that the most probable temperature fields sustaining atypical values of the global current can be naturally classified in an infinite set of curves, allowing us to exhaustively analyze their topological properties and to define universal profiles onto which all optimal fields collapse. We also compute the statistics of empirical heat current, where we find remarkable logarithmic tails for large current fluctuations orthogonal to the thermal gradient. Finally, we determine explicitly a number of cumulants of the current distribution, finding interesting relations between them.
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Affiliation(s)
- P L Garrido
- Departamento de Electromagnetismo y Física de la Materia, and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada. Spain
| | - P I Hurtado
- Departamento de Electromagnetismo y Física de la Materia, and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada. Spain
| | - N Tizón-Escamilla
- Departamento de Electromagnetismo y Física de la Materia, and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada. Spain
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7
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Tizón-Escamilla N, Pérez-Espigares C, Garrido PL, Hurtado PI. Order and Symmetry Breaking in the Fluctuations of Driven Systems. PHYSICAL REVIEW LETTERS 2017; 119:090602. [PMID: 28949563 DOI: 10.1103/physrevlett.119.090602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2016] [Indexed: 06/07/2023]
Abstract
Dynamical phase transitions (DPTs) in the space of trajectories are one of the most intriguing phenomena of nonequilibrium physics, but their nature in realistic high-dimensional systems remains puzzling. Here we observe for the first time a DPT in the current vector statistics of an archetypal two-dimensional (2D) driven diffusive system and characterize its properties using the macroscopic fluctuation theory. The complex interplay among the external field, anisotropy, and vector currents in 2D leads to a rich phase diagram, with different symmetry-broken fluctuation phases separated by lines of first- and second-order DPTs. Remarkably, different types of 1D order in the form of jammed density waves emerge to hinder transport for low-current fluctuations, revealing a connection between rare events and self-organized structures which enhance their probability.
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Affiliation(s)
- N Tizón-Escamilla
- Departamento de Electromagnetismo y Física de la Materia, and Institute Carlos I for Theoretical and Computational Physics, Universidad de Granada, Granada 18071, Spain
| | - C Pérez-Espigares
- University of Modena and Reggio Emilia, via G. Campi 213/b, 41125 Modena, Italy
- School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
| | - P L Garrido
- Departamento de Electromagnetismo y Física de la Materia, and Institute Carlos I for Theoretical and Computational Physics, Universidad de Granada, Granada 18071, Spain
| | - P I Hurtado
- Departamento de Electromagnetismo y Física de la Materia, and Institute Carlos I for Theoretical and Computational Physics, Universidad de Granada, Granada 18071, Spain
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8
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Tizón-Escamilla N, Hurtado PI, Garrido PL. Structure of the optimal path to a fluctuation. Phys Rev E 2017; 95:032119. [PMID: 28415174 DOI: 10.1103/physreve.95.032119] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2016] [Indexed: 11/07/2022]
Abstract
Macroscopic fluctuations have become an essential tool to understand physics far from equilibrium due to the link between their statistics and nonequilibrium ensembles. The optimal path leading to a fluctuation encodes key information on this problem, shedding light on, e.g., the physics behind the enhanced probability of rare events out of equilibrium, the possibility of dynamic phase transitions, and new symmetries. This makes the understanding of the properties of these optimal paths a central issue. Here we derive a fundamental relation which strongly constrains the architecture of these optimal paths for general d-dimensional nonequilibrium diffusive systems, and implies a nontrivial structure for the dominant current vector fields. Interestingly, this general relation (which encompasses and explains previous results) makes manifest the spatiotemporal nonlocality of the current statistics and the associated optimal trajectories.
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Affiliation(s)
- N Tizón-Escamilla
- Departamento de Electromagnetismo y Física de la Materia, and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada, Spain
| | - P I Hurtado
- Departamento de Electromagnetismo y Física de la Materia, and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada, Spain
| | - P L Garrido
- Departamento de Electromagnetismo y Física de la Materia, and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada, Spain
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