1
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Kumar V, Pal A, Shpielberg O. Emerging universality classes in thermally assisted activation of interacting diffusive systems: A perturbative hydrodynamic approach. J Chem Phys 2024; 160:134107. [PMID: 38563303 DOI: 10.1063/5.0195570] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2024] [Accepted: 03/01/2024] [Indexed: 04/04/2024] Open
Abstract
Thermal activation of a particle from a deep potential trap follows the Arrhenius law. Recently, this result has been generalized for interacting diffusive particles in the trap, revealing two universality classes-the Arrhenius class and the excluded volume class. The result was demonstrated with the aid of numerical analysis. Here, we present a perturbative hydrodynamic approach to analytically validate the existence and range of validity for the two universality classes.
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Affiliation(s)
- Vishwajeet Kumar
- 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
| | - 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 Ave. 199, Haifa 3498838, Israel
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2
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Krajenbrink A, Le Doussal P. Weak noise theory of the O'Connell-Yor polymer as an integrable discretization of the nonlinear Schrödinger equation. Phys Rev E 2024; 109:044109. [PMID: 38755892 DOI: 10.1103/physreve.109.044109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2023] [Accepted: 02/15/2024] [Indexed: 05/18/2024]
Abstract
We investigate and solve the weak noise theory for the semidiscrete O'Connell-Yor directed polymer. In the large deviation regime, the most probable evolution of the partition function obeys a classical nonlinear system which is a nonstandard discretization of the nonlinear Schrödinger equation with mixed initial-final conditions. We show that this system is integrable and find its general solution through an inverse scattering method and a non-standard Fredholm determinant framework that we develop. This allows us to obtain the large deviation rate function of the free energy of the polymer model from its conserved quantities and to study its convergence to the large deviations of the Kardar-Parisi-Zhang equation. Our model also degenerates to the classical Toda chain, which further substantiates the applicability of our Fredholm framework.
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Affiliation(s)
- Alexandre Krajenbrink
- Quantinuum, Terrington House, 13-15 Hills Road, Cambridge CB2 1NL, United Kingdom and Le Lab Quantique, 58 rue d'Hauteville, 75010 Paris, France
| | - Pierre Le Doussal
- Laboratoire de Physique de l'École Normale Supérieure, CNRS, ENS & PSL University, Sorbonne Université, Université de Paris, 75005 Paris, France
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3
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Chakraborty T, Pradhan P. Time-dependent properties of run-and-tumble particles. II. Current fluctuations. Phys Rev E 2024; 109:044135. [PMID: 38755901 DOI: 10.1103/physreve.109.044135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2023] [Accepted: 03/19/2024] [Indexed: 05/18/2024]
Abstract
We investigate steady-state current fluctuations in two models of hardcore run-and-tumble particles (RTPs) on a periodic one-dimensional lattice of L sites, for arbitrary tumbling rate γ=τ_{p}^{-1} and density ρ; model I consists of standard hardcore RTPs, while model II is an analytically tractable variant of model I, called a long-ranged lattice gas (LLG). We show that, in the limit of L large, the fluctuation of cumulative current Q_{i}(T,L) across the ith bond in a time interval T≫1/D grows first subdiffusively and then diffusively (linearly) with T: 〈Q_{i}^{2}〉∼T^{α} with α=1/2 for 1/D≪T≪L^{2}/D and α=1 for T≫L^{2}/D, where D(ρ,γ) is the collective- or bulk-diffusion coefficient; at small times T≪1/D, exponent α depends on the details. Remarkably, regardless of the model details, the scaled bond-current fluctuations D〈Q_{i}^{2}(T,L)〉/2χL≡W(y) as a function of scaled variable y=DT/L^{2} collapse onto a universal scaling curve W(y), where χ(ρ,γ) is the collective particle mobility. In the limit of small density and tumbling rate, ρ,γ→0, with ψ=ρ/γ fixed, there exists a scaling law: The scaled mobility γ^{a}χ(ρ,γ)/χ^{(0)}≡H(ψ) as a function of ψ collapses onto a scaling curve H(ψ), where a=1 and 2 in models I and II, respectively, and χ^{(0)} is the mobility in the limiting case of a symmetric simple exclusion process; notably, the scaling function H(ψ) is model dependent. For model II (LLG), we calculate exactly, within a truncation scheme, both the scaling functions, W(y) and H(ψ). We also calculate spatial correlation functions for the current and compare our theory with simulation results of model I; for both models, the correlation functions decay exponentially, with correlation length ξ∼τ_{p}^{1/2} diverging with persistence time τ_{p}≫1. Overall, our theory is in excellent agreement with simulations and complements the prior findings [T. Chakraborty and P. Pradhan, Phys. Rev. E 109, 024124 (2024)1539-375510.1103/PhysRevE.109.024124].
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Affiliation(s)
- Tanmoy Chakraborty
- Department of Physics of Complex Systems, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Punyabrata Pradhan
- Department of Physics of Complex Systems, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
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4
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Hartmann AK, Krajenbrink A, Le Doussal P. Probing the large deviations for the beta random walk in random medium. Phys Rev E 2024; 109:024122. [PMID: 38491613 DOI: 10.1103/physreve.109.024122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2023] [Accepted: 01/11/2024] [Indexed: 03/18/2024]
Abstract
We consider a discrete-time random walk on a one-dimensional lattice with space- and time-dependent random jump probabilities, known as the beta random walk. We are interested in the probability that, for a given realization of the jump probabilities (a sample), a walker starting at the origin at time t=0 is at position beyond ξsqrt[T/2] at time T. This probability fluctuates from sample to sample and we study the large-deviation rate function, which characterizes the tails of its distribution at large time T≫1. It is argued that, up to a simple rescaling, this rate function is identical to the one recently obtained exactly by two of the authors for the continuum version of the model. That continuum model also appears in the macroscopic fluctuation theory of a class of lattice gases, e.g., in the so-called KMP model of heat transfer. An extensive numerical simulation of the beta random walk, based on an importance sampling algorithm, is found in good agreement with the detailed analytical predictions. A first-order transition in the tilted measure, predicted to occur in the continuum model, is also observed in the numerics.
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Affiliation(s)
| | - Alexandre Krajenbrink
- Quantinuum, Terrington House, 13-15 Hills Road, Cambridge CB2 1NL, United Kingdom
- Le Lab Quantique, 58 rue d'Hauteville, 75010, Paris, France
| | - Pierre Le Doussal
- Laboratoire de Physique de l'École Normale Supérieure, PSL University, CNRS, Sorbonne Universités, 24 rue Lhomond, 75231 Paris, France
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5
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Jose S, Rosso A, Ramola K. Generalized disorder averages and current fluctuations in run and tumble particles. Phys Rev E 2023; 108:L052601. [PMID: 38115454 DOI: 10.1103/physreve.108.l052601] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Accepted: 11/07/2023] [Indexed: 12/21/2023]
Abstract
We present exact results for the fluctuations in the number of particles crossing the origin up to time t in a collection of noninteracting run and tumble particles in one dimension. In contrast to passive systems, such active particles are endowed with two inherent degrees of freedom, positions and velocities, which can be used to construct density and magnetization fields. We introduce generalized disorder averages associated with both these fields and perform annealed and quenched averages over various initial conditions. We show that the variance σ^{2} of the current in annealed versus quenched magnetization situations exhibits a surprising difference at short times, σ^{2}∼t vs σ^{2}∼t^{2}, respectively, with a sqrt[t] behavior emerging at large times. Our analytical results demonstrate that in the strictly quenched scenario, where both the density and magnetization fields are initially frozen, the fluctuations in the current are strongly suppressed. Importantly, these anomalous fluctuations cannot be obtained solely by freezing the density field.
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Affiliation(s)
- Stephy Jose
- Tata Institute of Fundamental Research, Hyderabad 500046, India
| | - Alberto Rosso
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Kabir Ramola
- Tata Institute of Fundamental Research, Hyderabad 500046, India
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6
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Sorkin B, Dean DS. Single-file diffusion in spatially inhomogeneous systems. Phys Rev E 2023; 108:054125. [PMID: 38115401 DOI: 10.1103/physreve.108.054125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Accepted: 09/06/2023] [Indexed: 12/21/2023]
Abstract
We study the effect of spatially varying potential and diffusivity on the dispersion of a tracer particle in single-file diffusion. Noninteracting particles in such a system exhibit normal diffusion at late times, which is characterized by an effective diffusion constant D_{eff}. Here we demonstrate the physically appealing result that the dispersion of single-file tracers in this system has the same long-time behavior as that for Brownian particles in a spatially homogeneous system with constant diffusivity D_{eff}. Our results are based on a late-time analysis of the Fokker-Planck equation, motivated by the mathematical theory of homogenization. The findings are confirmed by numerical simulations for both annealed and quenched initial conditions.
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Affiliation(s)
- Benjamin Sorkin
- School of Chemistry and Center for Physics and Chemistry of Living Systems, Tel Aviv University, 69978 Tel Aviv, Israel
| | - David S Dean
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
- Team MONC, INRIA Bordeaux Sud Ouest, CNRS UMR 5251, Bordeaux INP, Univ. Bordeaux, F-33400 Talence, France
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7
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Agranov T, Cates ME, Jack RL. Tricritical Behavior in Dynamical Phase Transitions. PHYSICAL REVIEW LETTERS 2023; 131:017102. [PMID: 37478424 DOI: 10.1103/physrevlett.131.017102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2022] [Revised: 03/31/2023] [Accepted: 05/23/2023] [Indexed: 07/23/2023]
Abstract
We identify a new scenario for dynamical phase transitions associated with time-integrated observables occurring in diffusive systems described by the macroscopic fluctuation theory. It is characterized by the pairwise meeting of first- and second-order bias-induced phase transition curves at two tricritical points. We formulate a simple, general criterion for its appearance and derive an exact Landau theory for the tricritical behavior. The scenario is demonstrated in three examples: the simple symmetric exclusion process biased by an activity-related structural observable; the Katz-Lebowitz-Spohn lattice gas model biased by its current; and in an active lattice gas biased by its entropy production.
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Affiliation(s)
- Tal Agranov
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, United Kingdom
| | - Michael E Cates
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, United Kingdom
| | - Robert L Jack
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, United Kingdom
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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8
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Di Bello C, Hartmann AK, Majumdar SN, Mori F, Rosso A, Schehr G. Current fluctuations in stochastically resetting particle systems. Phys Rev E 2023; 108:014112. [PMID: 37583217 DOI: 10.1103/physreve.108.014112] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2023] [Accepted: 04/28/2023] [Indexed: 08/17/2023]
Abstract
We consider a system of noninteracting particles on a line with initial positions distributed uniformly with density ρ on the negative half-line. We consider two different models: (i) Each particle performs independent Brownian motion with stochastic resetting to its initial position with rate r and (ii) each particle performs run-and-tumble motion, and with rate r its position gets reset to its initial value and simultaneously its velocity gets randomized. We study the effects of resetting on the distribution P(Q,t) of the integrated particle current Q up to time t through the origin (from left to right). We study both the annealed and the quenched current distributions and in both cases, we find that resetting induces a stationary limiting distribution of the current at long times. However, we show that the approach to the stationary state of the current distribution in the annealed and the quenched cases are drastically different for both models. In the annealed case, the whole distribution P_{an}(Q,t) approaches its stationary limit uniformly for all Q. In contrast, the quenched distribution P_{qu}(Q,t) attains its stationary form for QQ_{crit}(t). We show that Q_{crit}(t) increases linearly with t for large t. On the scale where Q∼Q_{crit}(t), we show that P_{qu}(Q,t) has an unusual large deviation form with a rate function that has a third-order phase transition at the critical point. We have computed the associated rate functions analytically for both models. Using an importance sampling method that allows to probe probabilities as tiny as 10^{-14000}, we were able to compute numerically this nonanalytic rate function for the resetting Brownian dynamics and found excellent agreement with our analytical prediction.
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Affiliation(s)
- Costantino Di Bello
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | | | - Satya N Majumdar
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Francesco Mori
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Alberto Rosso
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Grégory Schehr
- Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, 75252 Paris Cedex 05, France
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9
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Hurtado-Gutiérrez R, Hurtado PI, Pérez-Espigares C. Spectral signatures of symmetry-breaking dynamical phase transitions. Phys Rev E 2023; 108:014107. [PMID: 37583207 DOI: 10.1103/physreve.108.014107] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2023] [Accepted: 06/12/2023] [Indexed: 08/17/2023]
Abstract
Large deviation theory provides the framework to study the probability of rare fluctuations of time-averaged observables, opening new avenues of research in nonequilibrium physics. Some of the most appealing results within this context are dynamical phase transitions (DPTs), which might occur at the level of trajectories in order to maximize the probability of sustaining a rare event. While macroscopic fluctuation theory has underpinned much recent progress on the understanding of symmetry-breaking DPTs in driven diffusive systems, their microscopic characterization is still challenging. In this work we shed light on the general spectral mechanism giving rise to continuous DPTs not only for driven diffusive systems, but for any jump process in which a discrete Z_{n} symmetry is broken. By means of a symmetry-aided spectral analysis of the Doob-transformed dynamics, we provide the conditions whereby symmetry-breaking DPTs might emerge and how the different dynamical phases arise from the specific structure of the degenerate eigenvectors. In particular, we show explicitly how all symmetry-breaking features are encoded in the subleading eigenvectors of the degenerate subspace. Moreover, by partitioning configuration space into equivalence classes according to a proper order parameter, we achieve a substantial dimensional reduction which allows for the quantitative characterization of the spectral fingerprints of DPTs. We illustrate our predictions in several paradigmatic many-body systems, including (1) the one-dimensional boundary-driven weakly asymmetric exclusion process (WASEP), which exhibits a particle-hole symmetry-breaking DPT for current fluctuations, (2) the three- and four-state Potts model for spin dynamics, which displays discrete rotational symmetry-breaking DPTs for energy fluctuations, and (3) the closed WASEP which presents a continuous symmetry-breaking DPT into a time-crystal phase characterized by a rotating condensate.
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Affiliation(s)
- R Hurtado-Gutiérrez
- Institute Carlos I for Theoretical and Computational Physics, and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, Granada 18071, Spain
| | - P I Hurtado
- Institute Carlos I for Theoretical and Computational Physics, and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, Granada 18071, Spain
| | - C Pérez-Espigares
- Institute Carlos I for Theoretical and Computational Physics, and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, Granada 18071, Spain
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10
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Sakai I, Akimoto T. Sample-to-sample fluctuations of transport coefficients in the totally asymmetric simple exclusion process with quenched disorder. Phys Rev E 2023; 107:054131. [PMID: 37328985 DOI: 10.1103/physreve.107.054131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2023] [Accepted: 02/17/2023] [Indexed: 06/18/2023]
Abstract
We consider the totally asymmetric simple exclusion processes on quenched random energy landscapes. We show that the current and the diffusion coefficient differ from those for homogeneous environments. Using the mean-field approximation, we analytically obtain the site density when the particle density is low or high. As a result, the current and the diffusion coefficient are described by the dilute limit of particles or holes, respectively. However, in the intermediate regime, due to the many-body effect, the current and the diffusion coefficient differ from those for single-particle dynamics. The current is almost constant and becomes the maximal value in the intermediate regime. Moreover, the diffusion coefficient decreases with the particle density in the intermediate regime. We obtain analytical expressions for the maximal current and the diffusion coefficient based on the renewal theory. The deepest energy depth plays a central role in determining the maximal current and the diffusion coefficient. As a result, the maximal current and the diffusion coefficient depend crucially on the disorder, i.e., non-self-averaging. Based on the extreme value theory, we find that sample-to-sample fluctuations of the maximal current and diffusion coefficient are characterized by the Weibull distribution. We show that the disorder averages of the maximal current and the diffusion coefficient converge to zero as the system size is increased and quantify the degree of the non-self-averaging effect for the maximal current and the diffusion coefficient.
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Affiliation(s)
- Issei Sakai
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
| | - Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
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11
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Sakai I, Akimoto T. Non-self-averaging of current in a totally asymmetric simple exclusion process with quenched disorder. Phys Rev E 2023; 107:L052103. [PMID: 37329050 DOI: 10.1103/physreve.107.l052103] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2022] [Accepted: 05/01/2023] [Indexed: 06/18/2023]
Abstract
We investigate the current properties in the totally asymmetric simple exclusion process (TASEP) on a quenched random energy landscape. In low- and high-density regimes, the properties are characterized by single-particle dynamics. In the intermediate one, the current becomes constant and is maximized. Based on the renewal theory, we derive accurate results for the maximum current. The maximum current significantly depends on a disorder realization, i.e., non-self-averaging (SA). We demonstrate that the disorder average of the maximum current decreases with the system size, and the sample-to-sample fluctuations of the maximum current exceed those of current in the low- and high-density regimes. We find a significant difference between single-particle dynamics and the TASEP. In particular, the non-SA behavior of the maximum current is always observed, whereas the transition from non-SA to SA for current in single-particle dynamics exists.
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Affiliation(s)
- Issei Sakai
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
| | - Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
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12
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Krajenbrink A, Le Doussal P. Crossover from the macroscopic fluctuation theory to the Kardar-Parisi-Zhang equation controls the large deviations beyond Einstein's diffusion. Phys Rev E 2023; 107:014137. [PMID: 36797871 DOI: 10.1103/physreve.107.014137] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2022] [Accepted: 12/21/2022] [Indexed: 01/30/2023]
Abstract
We study the crossover from the macroscopic fluctuation theory (MFT), which describes one-dimensional stochastic diffusive systems at late times, to the weak noise theory (WNT), which describes the Kardar-Parisi-Zhang (KPZ) equation at early times. We focus on the example of the diffusion in a time-dependent random field, observed in an atypical direction which induces an asymmetry. The crossover is described by a nonlinear system which interpolates between the derivative and the standard nonlinear Schrodinger equations in imaginary time. We solve this system using the inverse scattering method for mixed-time boundary conditions introduced by us to solve the WNT. We obtain the rate function which describes the large deviations of the sample-to-sample fluctuations of the cumulative distribution of the tracer position. It exhibits a crossover as the asymmetry is varied, recovering both MFT and KPZ limits. We sketch how it is consistent with extracting the asymptotics of a Fredholm determinant formula, recently derived for sticky Brownian motions. The crossover mechanism studied here should generalize to a larger class of models described by the MFT. Our results apply to study extremal diffusion beyond Einstein's theory.
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Affiliation(s)
| | - Pierre Le Doussal
- Laboratoire de Physique de l'École Normale Supérieure, CNRS, ENS & PSL University, Sorbonne Université, Université de Paris, 75005 Paris, France
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13
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Rana J, Sadhu T. Large deviations of a tracer position in the dense and the dilute limits of single-file diffusion. Phys Rev E 2023; 107:L012101. [PMID: 36797963 DOI: 10.1103/physreve.107.l012101] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2022] [Accepted: 01/04/2023] [Indexed: 06/18/2023]
Abstract
We apply the macroscopic fluctuation theory to analyze the long-time statistics of the position of a tracer in the dense and the dilute limits of diffusive single-file systems. Our explicit results are about the corresponding large deviation functions for an initial step density profile with the fluctuating (annealed) and the fixed (quenched) initial conditions. These hydrodynamic results are applicable for a general single-file system and they agree with recent exact results obtained by microscopic solutions for specific model systems.
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Affiliation(s)
- Jagannath Rana
- Department of Theoretical Physics, Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Mumbai 400005, India
| | - Tridib Sadhu
- Department of Theoretical Physics, Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Mumbai 400005, India
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14
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Dieball C, Godec A. Mathematical, Thermodynamical, and Experimental Necessity for Coarse Graining Empirical Densities and Currents in Continuous Space. PHYSICAL REVIEW LETTERS 2022; 129:140601. [PMID: 36240401 DOI: 10.1103/physrevlett.129.140601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2021] [Revised: 07/19/2022] [Accepted: 07/28/2022] [Indexed: 06/16/2023]
Abstract
We present general results on fluctuations and spatial correlations of the coarse-grained empirical density and current of Markovian diffusion in equilibrium or nonequilibrium steady states on all timescales. We unravel a deep connection between current fluctuations and generalized time-reversal symmetry, providing new insight into time-averaged observables. We highlight the essential role of coarse graining in space from mathematical, thermodynamical, and experimental points of view. Spatial coarse graining is required to uncover salient features of currents that break detailed balance, and a thermodynamically "optimal" coarse graining ensures the most precise inference of dissipation. Defined without coarse graining, the fluctuations of empirical density and current are proven to diverge on all timescales in dimensions higher than one, which has far-reaching consequences for the central-limit regime in continuous space. We apply the results to examples of irreversible diffusion. Our findings provide new intuition about time-averaged observables and allow for a more efficient analysis of single-molecule experiments.
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Affiliation(s)
- Cai Dieball
- Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, Am Faßberg 11, 37077 Göttingen
| | - Aljaž Godec
- Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, Am Faßberg 11, 37077 Göttingen
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15
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Horii H, Lefevere R, Itami M, Nemoto T. Anomalous fluctuations of renewal-reward processes with heavy-tailed distributions. Phys Rev E 2022; 106:034130. [PMID: 36266861 DOI: 10.1103/physreve.106.034130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2022] [Accepted: 09/07/2022] [Indexed: 06/16/2023]
Abstract
For renewal-reward processes with a power-law decaying waiting time distribution, anomalously large probabilities are assigned to atypical values of the asymptotic processes. Previous works have revealed that this anomalous scaling causes a singularity in the corresponding large deviation function. In order to further understand this problem, we study in this article the scaling of variance in several renewal-reward processes: counting processes with two different power-law decaying waiting time distributions and a Knudsen gas (a heat conduction model). Through analytical and numerical analyses of these models, we find that the variances show an anomalous scaling when the exponent of the power law is -3. For a counting process with the power-law exponent smaller than -3, this anomalous scaling does not take place: this indicates that if we only consider the standard deviation from the expectation, any anomalous behavior will not be detected. In this case, we argue that anomalous scaling appears in higher order cumulants. Finally, many-body particles interacting through soft-core interactions with the boundary conditions employed in the Knudsen gas are studied using numerical simulations. We observe that the variance scaling becomes normal even though the power-law exponent in the boundary conditions is -3.
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Affiliation(s)
- Hiroshi Horii
- Université Paris Cité, Laboratoire de Probabilités, Statistiques et Modélisation, UMR 8001, F-75205 Paris, France
| | - Raphaël Lefevere
- Université Paris Cité, Laboratoire de Probabilités, Statistiques et Modélisation, UMR 8001, F-75205 Paris, France
| | - Masato Itami
- Center for Science Adventure and Collaborative Research Advancement, Kyoto University, Kyoto 606-8502, Japan
| | - Takahiro Nemoto
- Graduate School of Informatics, Kyoto University, Yoshida Hon-machi, Sakyo-ku, Kyoto 606-8501, Japan
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16
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Bettelheim E, Smith NR, Meerson B. Inverse Scattering Method Solves the Problem of Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model. PHYSICAL REVIEW LETTERS 2022; 128:130602. [PMID: 35426706 DOI: 10.1103/physrevlett.128.130602] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2021] [Revised: 02/01/2022] [Accepted: 03/08/2022] [Indexed: 06/14/2023]
Abstract
We determine the full statistics of nonstationary heat transfer in the Kipnis-Marchioro-Presutti lattice gas model at long times by uncovering and exploiting complete integrability of the underlying equations of the macroscopic fluctuation theory. These equations are closely related to the derivative nonlinear Schrödinger equation (DNLS), and we solve them by the Zakharov-Shabat inverse scattering method (ISM) adapted by D. J. Kaup and A. C. Newell, J. Math. Phys. 19, 798 (1978)JMAPAQ0022-248810.1063/1.523737 for the DNLS. We obtain explicit results for the exact large deviation function of the transferred heat for an initially localized heat pulse, where we uncover a nontrivial symmetry relation.
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Affiliation(s)
- Eldad Bettelheim
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 9190401, Israel
| | - Naftali R Smith
- Laboratoire de Physique de l'École Normale Supérieure, CNRS, ENS & Université PSL, Sorbonne Université, Université de Paris, 75005 Paris, France
- Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer, 8499000, Israel
| | - Baruch Meerson
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 9190401, Israel
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17
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Grabsch A, Poncet A, Rizkallah P, Illien P, Bénichou O. Exact closure and solution for spatial correlations in single-file diffusion. SCIENCE ADVANCES 2022; 8:eabm5043. [PMID: 35333581 PMCID: PMC8956262 DOI: 10.1126/sciadv.abm5043] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2021] [Accepted: 02/02/2022] [Indexed: 05/29/2023]
Abstract
In single-file transport particles diffuse in narrow channels while not overtaking each other. it is a fundamental model for the tracer subdiffusion observed in confined systems, such as zeolites or carbon nanotubes. This anomalous behavior originates from strong bath-tracer correlations in one dimension. Despite extensive effort, these remained elusive, because they involve an infinite hierarchy of equations. For the symmetric exclusion process, a paradigmatic model of single-file diffusion, we break the hierarchy to unveil and solve a closed exact equation satisfied by these correlations. Beyond quantifying the correlations, the role of this key equation as a tool for interacting particle systems is further demonstrated by its application to out-of-equilibrium situations, other observables, and other representative single-file systems.
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Affiliation(s)
- Aurélien Grabsch
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), 4 Place Jussieu, 75005 Paris, France
| | - Alexis Poncet
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), 4 Place Jussieu, 75005 Paris, France
- Université Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Pierre Rizkallah
- Sorbonne Université, CNRS, Laboratoire de Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 4 Place Jussieu, 75005 Paris, France
| | - Pierre Illien
- Sorbonne Université, CNRS, Laboratoire de Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 4 Place Jussieu, 75005 Paris, France
| | - Olivier Bénichou
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), 4 Place Jussieu, 75005 Paris, France
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18
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Hartmann AK, Meerson B, Sasorov P. Observing symmetry-broken optimal paths of the stationary Kardar-Parisi-Zhang interface via a large-deviation sampling of directed polymers in random media. Phys Rev E 2021; 104:054125. [PMID: 34942795 DOI: 10.1103/physreve.104.054125] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2021] [Accepted: 11/03/2021] [Indexed: 11/07/2022]
Abstract
Consider the short-time probability distribution P(H,t) of the one-point interface height difference h(x=0,τ=t)-h(x=0,τ=0)=H of the stationary interface h(x,τ) described by the Kardar-Parisi-Zhang (KPZ) equation. It was previously shown that the optimal path, the most probable history of the interface h(x,τ) which dominates the upper tail of P(H,t), is described by any of two ramplike structures of h(x,τ) traveling either to the left, or to the right. These two solutions emerge, at a critical value of H, via a spontaneous breaking of the mirror symmetry x↔-x of the optimal path, and this symmetry breaking is responsible for a second-order dynamical phase transition in the system. We simulate the interface configurations numerically by employing a large-deviation Monte Carlo sampling algorithm in conjunction with the mapping between the KPZ interface and the directed polymer in a random potential at high temperature. This allows us to observe the optimal paths, which determine each of the two tails of P(H,t), down to probability densities as small as 10^{-500}. At short times we observe mirror-symmetry-broken traveling optimal paths for the upper tail, and a single mirror-symmetric path for the lower tail, in good quantitative agreement with analytical predictions. At long times, even at moderate values of H, where the optimal fluctuation method is not supposed to apply, we still observe two well-defined dominating paths. Each of them violates the mirror symmetry x↔-x and is a mirror image of the other.
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Affiliation(s)
| | - Baruch Meerson
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Pavel Sasorov
- Institute of Physics CAS-ELI Beamlines, 182 21 Prague, Czech Republic.,Keldysh Institute of Applied Mathematics, Moscow 125047, Russia
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19
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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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20
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Bernard D, Piroli L. Entanglement distribution in the quantum symmetric simple exclusion process. Phys Rev E 2021; 104:014146. [PMID: 34412369 DOI: 10.1103/physreve.104.014146] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2021] [Accepted: 07/07/2021] [Indexed: 11/07/2022]
Abstract
We study the probability distribution of entanglement in the quantum symmetric simple exclusion process, a model of fermions hopping with random Brownian amplitudes between neighboring sites. We consider a protocol where the system is initialized in a pure product state of M particles, and we focus on the late-time distribution of Rényi-q entropies for a subsystem of size ℓ. By means of a Coulomb gas approach from random matrix theory, we compute analytically the large-deviation function of the entropy in the thermodynamic limit. For q>1, we show that, depending on the value of the ratio ℓ/M, the entropy distribution displays either two or three distinct regimes, ranging from low to high entanglement. These are connected by points where the probability density features singularities in its third derivative, which can be understood in terms of a transition in the corresponding charge density of the Coulomb gas. Our analytic results are supported by numerical Monte Carlo simulations.
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Affiliation(s)
- Denis Bernard
- Laboratoire de Physique de l'École Normale Supérieure, CNRS, ENS & PSL University, Sorbonne Université, Université de Paris, 75005 Paris, France
| | - Lorenzo Piroli
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology, Schellingstraße 4, 80799 München, Germany
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21
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Dolezal J, Jack RL. Long-ranged correlations in large deviations of local clustering. Phys Rev E 2021; 103:052132. [PMID: 34134232 DOI: 10.1103/physreve.103.052132] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2020] [Accepted: 04/19/2021] [Indexed: 11/07/2022]
Abstract
In systems of diffusing particles, we investigate large deviations of a time-averaged measure of clustering around one particle. We focus on biased ensembles of trajectories, which realize large-deviation events. The bias acts on a single particle, but elicits a response that spans the whole system. We analyze this effect through the lens of macroscopic fluctuation theory, focusing on the coupling of the bias to hydrodynamic modes. This explains that the dynamical free energy has nontrivial scaling relationships with the system size, in 1 and 2 spatial dimensions. We show that the long-ranged response to a bias on one particle also has consequences when biasing two particles.
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Affiliation(s)
- Jakub Dolezal
- DAMTP, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Robert L Jack
- DAMTP, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.,Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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22
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Hurtado-Gutiérrez R, Carollo F, Pérez-Espigares C, Hurtado PI. Building Continuous Time Crystals from Rare Events. PHYSICAL REVIEW LETTERS 2020; 125:160601. [PMID: 33124846 DOI: 10.1103/physrevlett.125.160601] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2019] [Accepted: 09/17/2020] [Indexed: 06/11/2023]
Abstract
Symmetry-breaking dynamical phase transitions (DPTs) abound in the fluctuations of nonequilibrium systems. Here, we show that the spectral features of a particular class of DPTs exhibit the fingerprints of the recently discovered time-crystal phase of matter. Using Doob's transform as a tool, we provide a mechanism to build classical time-crystal generators from the rare event statistics of some driven diffusive systems. An analysis of the Doob's smart field in terms of the order parameter of the transition then leads to the time-crystal lattice gas (TCLG), a model of driven fluid subject to an external packing field, which presents a clear-cut steady-state phase transition to a time-crystalline phase characterized by a matter density wave, which breaks continuous time-translation symmetry and displays rigidity and long-range spatiotemporal order, as required for a time crystal. A hydrodynamic analysis of the TCLG transition uncovers striking similarities, but also key differences, with the Kuramoto synchronization transition. Possible experimental realizations of the TCLG in colloidal fluids are also discussed.
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Affiliation(s)
- R Hurtado-Gutiérrez
- 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
| | - F Carollo
- Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - C 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
| | - P I Hurtado
- 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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23
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Jin T, Krajenbrink A, Bernard D. From Stochastic Spin Chains to Quantum Kardar-Parisi-Zhang Dynamics. PHYSICAL REVIEW LETTERS 2020; 125:040603. [PMID: 32794778 DOI: 10.1103/physrevlett.125.040603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2020] [Accepted: 06/16/2020] [Indexed: 06/11/2023]
Abstract
We introduce the asymmetric extension of the quantum symmetric simple exclusion process which is a stochastic model of fermions on a lattice hopping with random amplitudes. In this setting, we analytically show that the time-integrated current of fermions defines a height field that exhibits quantum nonlinear stochastic Kardar-Parisi-Zhang dynamics. Similarly to classical simple exclusion processes, we further introduce the discrete Cole-Hopf (or Gärtner) transform of the height field that satisfies a quantum version of the stochastic heat equation. Finally, we investigate the limit of the height field theory in the continuum under the celebrated Kardar-Parisi-Zhang scaling and the regime of almost-commuting quantum noise.
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Affiliation(s)
- Tony Jin
- DQMP, University of Geneva, 24 Quai Ernest-Ansermet, CH-1211 Geneva, Switzerland
- Laboratoire de Physique de l'École Normale Supérieure, CNRS, ENS & PSL University, Sorbonne Université, Université de Paris, 75005 Paris, France
| | - Alexandre Krajenbrink
- Laboratoire de Physique de l'École Normale Supérieure, CNRS, ENS & PSL University, Sorbonne Université, Université de Paris, 75005 Paris, France
- Scuola Internazionale Superiore di Studi Avanzati and Istituto Nazionale di Fisica Nucleare, via Bonomea 265, 34136 Trieste, Italy
- Cambridge Quantum Computing Ltd, 9a Bridge Street, CB2 1UB Cambridge, United Kingdom
| | - Denis Bernard
- Laboratoire de Physique de l'École Normale Supérieure, CNRS, ENS & PSL University, Sorbonne Université, Université de Paris, 75005 Paris, France
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24
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Banerjee T, Majumdar SN, Rosso A, Schehr G. Current fluctuations in noninteracting run-and-tumble particles in one dimension. Phys Rev E 2020; 101:052101. [PMID: 32575200 DOI: 10.1103/physreve.101.052101] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2020] [Accepted: 03/30/2020] [Indexed: 06/11/2023]
Abstract
We present a general framework to study the distribution of the flux through the origin up to time t, in a noninteracting one-dimensional system of particles with a step initial condition with a fixed density ρ of particles to the left of the origin. We focus principally on two cases: (i) particles undergoing diffusive dynamics (passive case) and (ii) run-and-tumble dynamics for each particle (active case). In analogy with disordered systems, we consider the flux distribution for both the annealed and the quenched initial conditions, for passive and active particles. In the annealed case, we show that, for arbitrary particle dynamics, the flux distribution is a Poissonian with a mean μ(t) that we compute exactly in terms of the Green's function of the single-particle dynamics. For the quenched case, we show that, for the run-and-tumble dynamics, the quenched flux distribution takes an anomalous large-deviation form at large times, P_{qu}(Q,t)∼exp[-ρv_{0}γt^{2}ψ_{RTP}(Q/ρv_{0}t)], where γ is the rate of tumbling and v_{0} is the ballistic speed between two successive tumblings. In this paper, we compute the rate function ψ_{RTP}(q) and show that it is nontrivial. Our method also gives access to the probability of the rare event that, at time t, there is no particle to the right of the origin. For diffusive and run-and-tumble dynamics, we find that this probability decays with time as a stretched exponential, ∼exp(-csqrt[t]), where the constant c can be computed exactly. We verify our results for these large deviations by using an importance sampling Monte Carlo method.
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Affiliation(s)
- Tirthankar Banerjee
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
- Instituut voor Theoretische Fysica, KU Leuven, 3001 Heverlee, Belgium
| | - Satya N Majumdar
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Alberto Rosso
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Grégory Schehr
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
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25
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Vasiloiu LM, Oakes THE, Carollo F, Garrahan JP. Trajectory phase transitions in noninteracting spin systems. Phys Rev E 2020; 101:042115. [PMID: 32422782 DOI: 10.1103/physreve.101.042115] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2019] [Accepted: 02/17/2020] [Indexed: 11/07/2022]
Abstract
We show that a collection of independent Ising spins evolving stochastically can display surprisingly large fluctuations toward ordered behavior, as quantified by certain types of time-integrated plaquette observables, despite the underlying dynamics being noninteracting. In the large-deviation (LD) regime of long times and large system size, this can give rise to a phase transition in trajectory space. As a noninteracting system we consider a collection of spins undergoing single spin-flip dynamics at infinite temperature. For the dynamical observables we study, the associated tilted generators have an exact and explicit spin-plaquette duality. Such setup suggests the existence of a transition (in the large size limit) at the self-dual point of the tilted generator. The nature of the LD transition depends on the observable. We consider explicitly two situations: (i) for a pairwise bond observable the LD transition is continuous and equivalent to that of the transverse field Ising model and (ii) for a higher-order plaquette observable, in contrast, the LD transition is first order. Case (i) is easy to prove analytically, while we confirm case (ii) numerically via an efficient trajectory sampling scheme that exploits the noninteracting nature of the original dynamics.
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Affiliation(s)
- Loredana M Vasiloiu
- 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
| | - Tom H E Oakes
- 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
| | - Federico Carollo
- 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.,Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Juan P Garrahan
- 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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26
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Polychronakos AP. Solitons in fluctuating hydrodynamics of diffusive processes. Phys Rev E 2020; 101:022209. [PMID: 32168645 DOI: 10.1103/physreve.101.022209] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2019] [Accepted: 01/29/2020] [Indexed: 11/07/2022]
Abstract
We demonstrate that fluid mechanical systems arising from large fluctuations of one-dimensional statistical processes generically exhibit solitons and nonlinear waves. We derive the explicit form of these solutions and examine their properties for the specific cases of the Kipnis-Marchioro-Presutti model (KMP) and the symmetric exclusion process (SEP). We show that the two fluid systems are related by a nonlinear transformation but still have markedly different properties. In particular, the KMP fluid has a nontrivial sound wave spectrum exhibiting birefringence, whereas sound waves for the SEP fluid are essentially trivial. The appearance of sound waves and soliton configurations in the KMP model is related to the onset of instabilities.
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Affiliation(s)
- Alexios P Polychronakos
- Department of Physics, The City College of New York, New York 10031, USA and The Graduate Center, CUNY, New York, New York 10016, USA
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27
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Lips D, Ryabov A, Maass P. Single-file transport in periodic potentials: The Brownian asymmetric simple exclusion process. Phys Rev E 2019; 100:052121. [PMID: 31869987 DOI: 10.1103/physreve.100.052121] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2019] [Indexed: 06/10/2023]
Abstract
Single-file Brownian motion in periodic structures is an important process in nature and technology, which becomes increasingly amenable for experimental investigation under controlled conditions. To explore and understand generic features of this motion, the Brownian asymmetric simple exclusion process (BASEP) was recently introduced. The BASEP refers to diffusion models where hard spheres are driven by a constant drag force through a periodic potential. Here we derive general properties of the rich collective dynamics in the BASEP. Average currents in the steady state change dramatically with the particle size and density. For an open system coupled to particle reservoirs, extremal current principles predict various nonequilibrium phases, which we verify by Brownian dynamics simulations. For general pair interactions we discuss connections to single-file transport by traveling-wave potentials and prove the impossibility of current reversals in systems driven by a constant drag and by traveling waves.
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Affiliation(s)
- Dominik Lips
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
| | - Artem Ryabov
- Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, CZ-18000 Praha 8, Czech Republic
- Centro de Física Teórica e Computacional, Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande P-1749-016 Lisboa, Portugal
| | - Philipp Maass
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
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28
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Bernard D, Jin T. Open Quantum Symmetric Simple Exclusion Process. PHYSICAL REVIEW LETTERS 2019; 123:080601. [PMID: 31491217 DOI: 10.1103/physrevlett.123.080601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2019] [Indexed: 06/10/2023]
Abstract
We present the solution to a model of fermions hopping between neighboring sites on a line with random Brownian amplitudes and open boundary conditions driving the system out of equilibrium. The average dynamics reduces to that of the symmetric simple exclusion process. However, the full distribution encodes for a richer behavior, entailing fluctuating quantum coherences which survive in the steady limit. We determine exactly the steady statistical distribution of the system state. We show that the out-of-equilibrium quantum coherence fluctuations satisfy a large-deviation principle, and we present a method to recursively compute exactly the large-deviation function. As a by-product, our approach gives a solution of the classical symmetric simple exclusion process based on fermion technology. Our results open the route towards the extension of the macroscopic fluctuation theory to many-body quantum systems.
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Affiliation(s)
- Denis Bernard
- Laboratoire de Physique de l'Ecole Normale Supérieure de Paris, CNRS, ENS & Université PSL, Sorbonne Université, Université Paris Diderot, 75005 France
| | - Tony Jin
- Laboratoire de Physique de l'Ecole Normale Supérieure de Paris, CNRS, ENS & Université PSL, Sorbonne Université, Université Paris Diderot, 75005 France
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29
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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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30
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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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31
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Nemoto T, Fodor É, Cates ME, Jack RL, Tailleur J. Optimizing active work: Dynamical phase transitions, collective motion, and jamming. Phys Rev E 2019; 99:022605. [PMID: 30934223 DOI: 10.1103/physreve.99.022605] [Citation(s) in RCA: 38] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2018] [Indexed: 06/09/2023]
Abstract
Active work measures how far the local self-forcing of active particles translates into real motion. Using population Monte Carlo methods, we investigate large deviations in the active work for repulsive active Brownian disks. Minimizing the active work generically results in dynamical arrest; in contrast, despite the lack of aligning interactions, trajectories of high active work correspond to a collectively moving, aligned state. We use heuristic and analytic arguments to explain the origin of dynamical phase transitions separating the arrested, typical, and aligned regimes.
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Affiliation(s)
- Takahiro Nemoto
- Philippe Meyer Institute for Theoretical Physics, Physics Department, École Normale Supérieure & PSL Research University, 24 rue Lhomond, 75231 Paris Cedex 05, France
| | - Étienne Fodor
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Michael E Cates
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Robert L Jack
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Julien Tailleur
- Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS/P7, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, 75205 Paris cedex 13, France
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32
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Lips D, Ryabov A, Maass P. Brownian Asymmetric Simple Exclusion Process. PHYSICAL REVIEW LETTERS 2018; 121:160601. [PMID: 30387631 DOI: 10.1103/physrevlett.121.160601] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2018] [Indexed: 06/08/2023]
Abstract
We study the driven Brownian motion of hard rods in a one-dimensional cosine potential with a large amplitude compared to the thermal energy. In a closed system, we find surprising features of the steady-state current in dependence of the particle density. The form of the current-density relation changes greatly with the particle size and can exhibit both a local maximum and minimum. The changes are caused by an interplay of a barrier reduction, blocking, and exchange symmetry effect. The latter leads to a current equal to that of noninteracting particles for a particle size commensurate with the period length of the cosine potential. For an open system coupled to particle reservoirs, we predict five different phases of nonequilibrium steady states to occur. Our results show that the particle size can be of crucial importance for nonequilibrium phase transitions in driven systems. Possible experiments for demonstrating our findings are pointed out.
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Affiliation(s)
- Dominik Lips
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
| | - Artem Ryabov
- Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, CZ-18000 Praha 8, Czech Republic
| | - Philipp Maass
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
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33
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Renger DRM. Gradient and GENERIC Systems in the Space of Fluxes, Applied to Reacting Particle Systems. ENTROPY 2018; 20:e20080596. [PMID: 33265685 PMCID: PMC7513121 DOI: 10.3390/e20080596] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/02/2018] [Revised: 08/02/2018] [Accepted: 08/08/2018] [Indexed: 11/26/2022]
Abstract
In a previous work we devised a framework to derive generalised gradient systems for an evolution equation from the large deviations of an underlying microscopic system, in the spirit of the Onsager–Machlup relations. Of particular interest is the case where the microscopic system consists of random particles, and the macroscopic quantity is the empirical measure or concentration. In this work we take the particle flux as the macroscopic quantity, which is related to the concentration via a continuity equation. By a similar argument the large deviations can induce a generalised gradient or GENERIC system in the space of fluxes. In a general setting we study how flux gradient or GENERIC systems are related to gradient systems of concentrations. This shows that many gradient or GENERIC systems arise from an underlying gradient or GENERIC system where fluxes rather than densities are being driven by (free) energies. The arguments are explained by the example of reacting particle systems, which is later expanded to include spatial diffusion as well.
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34
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Shpielberg O. Geometrical interpretation of dynamical phase transitions in boundary-driven systems. Phys Rev E 2017; 96:062108. [PMID: 29347441 DOI: 10.1103/physreve.96.062108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2017] [Indexed: 06/07/2023]
Abstract
Dynamical phase transitions are defined as nonanalytic points of the large deviation function of current fluctuations. We show that for boundary-driven systems, many dynamical phase transitions can be identified using the geometrical structure of an effective potential of a Hamiltonian, recovered from the macroscopic fluctuation theory description. Using this method we identify new dynamical phase transitions that could not be recovered using existing perturbative methods. Moreover, using the Hamiltonian picture, an experimental scheme is suggested to demonstrate an analog of dynamical phase transitions in linear, rather than exponential, time.
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Affiliation(s)
- Ohad Shpielberg
- Laboratoire de Physique Théorique de l'École Normale Supérieure de Paris, CNRS, ENS & PSL Research University, UPMC & Sorbonne Universités, 75005 Paris, France
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35
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Manacorda A, Puglisi A. Lattice Model to Derive the Fluctuating Hydrodynamics of Active Particles with Inertia. PHYSICAL REVIEW LETTERS 2017; 119:208003. [PMID: 29219378 DOI: 10.1103/physrevlett.119.208003] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2017] [Indexed: 05/20/2023]
Abstract
We derive the hydrodynamic equations with fluctuating currents for the density, momentum, and energy fields for an active system in the dilute limit. In our model, nonoverdamped self-propelled particles (such as grains or birds) move on a lattice, interacting by means of aligning dissipative forces and excluded volume repulsion. Our macroscopic equations, in a specific case, reproduce a transition line from a disordered phase to a swarming phase and a linear dispersion law accounting for underdamped wave propagation. Numerical simulations up to a packing fraction ∼10% are in fair agreement with the theory, including the macroscopic noise amplitudes. At a higher packing fraction, a dense-diluted coexistence emerges. We underline the analogies with the granular kinetic theories, elucidating the relation between the active swarming phase and granular shear instability.
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Affiliation(s)
- A Manacorda
- Dipartimento di Fisica, Sapienza Università di Roma, piazzale A. Moro 2, 00185 Roma, Italy
- CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, piazzale A. Moro 2, 00185 Roma, Italy
| | - A Puglisi
- CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, piazzale A. Moro 2, 00185 Roma, Italy
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36
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The exact phase diagram for a class of open multispecies asymmetric exclusion processes. Sci Rep 2017; 7:13555. [PMID: 29051504 PMCID: PMC5648981 DOI: 10.1038/s41598-017-12768-8] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2017] [Accepted: 09/14/2017] [Indexed: 11/21/2022] Open
Abstract
The asymmetric exclusion process is an idealised stochastic model of transport, whose exact solution has given important insight into a general theory of nonequilibrium statistical physics. In this work, we consider a totally asymmetric exclusion process with multiple species of particles on a one-dimensional lattice in contact with reservoirs. We derive the exact nonequilibrium phase diagram for the system in the long time limit. We find two new phenomena in certain regions of the phase diagram: dynamical expulsion when the density of a species becomes zero throughout the system, and dynamical localisation when the density of a species is nonzero only within an interval far from the boundaries. We give a complete explanation of the macroscopic features of the phase diagram using what we call nested fat shocks.
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37
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Cagnetta F, Corberi F, Gonnella G, Suma A. Large Fluctuations and Dynamic Phase Transition in a System of Self-Propelled Particles. PHYSICAL REVIEW LETTERS 2017; 119:158002. [PMID: 29077467 DOI: 10.1103/physrevlett.119.158002] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2016] [Indexed: 06/07/2023]
Abstract
We study the statistics, in stationary conditions, of the work W_{τ} done by the active force in different systems of self-propelled particles in a time τ. We show the existence of a critical value W_{τ}^{†} such that fluctuations with W_{τ}>W_{τ}^{†} correspond to configurations where interaction between particles plays a minor role whereas those with W_{τ}<W_{τ}^{†} represent states with single particles dragged by clusters. This twofold behavior is fully mirrored by the probability distribution P(W_{τ}) of the work, which does not obey the large-deviation principle for W_{τ}<W_{τ}^{†}. This pattern of behavior can be interpreted as due to a phase transition occurring at the level of fluctuating quantities and an order parameter is correspondingly identified.
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Affiliation(s)
- F Cagnetta
- Dipartimento di Fisica, Università di Bari, and Sezione INFN di Bari, via Amendola 173, 70126 Bari, Italy
| | - F Corberi
- Dipartimento di Fisica E.R.Caianiello and INFN, Gruppo Collegato di Salerno, and CNISM, Unità di Salerno, Università di Salerno, via Giovanni Paolo II 132, 8408 Fisciano (SA), Italy
| | - G Gonnella
- Dipartimento di Fisica, Università di Bari, and Sezione INFN di Bari, via Amendola 173, 70126 Bari, Italy
| | - A Suma
- SISSA Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy
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38
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Agranov T, Meerson B. Fluctuations of absorption of interacting diffusing particles by multiple absorbers. Phys Rev E 2017; 95:062124. [PMID: 28709351 DOI: 10.1103/physreve.95.062124] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2017] [Indexed: 11/07/2022]
Abstract
We study fluctuations of particle absorption by a three-dimensional domain with multiple absorbing patches. The domain is in contact with a gas of interacting diffusing particles. This problem is motivated by living cell sensing via multiple receptors distributed over the cell surface. Employing the macroscopic fluctuation theory, we calculate the covariance matrix of the particle absorption by different patches, extending previous works which addressed fluctuations of a single current. We find a condition when the sign of correlations between different patches is fully determined by the transport coefficients of the gas and is independent of the problem's geometry. We show that the fluctuating particle flux field typically develops vorticity. We establish a simple connection between the statistics of particle absorption by all the patches combined and the statistics of current in a nonequilibrium steady state in one dimension. We also discuss connections between the absorption statistics and (i) statistics of electric currents in multiterminal diffusive conductors and (ii) statistics of wave transmission through disordered media with multiple absorbers.
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Affiliation(s)
- Tal Agranov
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Baruch Meerson
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
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39
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Nemoto T, Jack RL, Lecomte V. Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model. PHYSICAL REVIEW LETTERS 2017; 118:115702. [PMID: 28368624 DOI: 10.1103/physrevlett.118.115702] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2016] [Indexed: 06/07/2023]
Abstract
We analyze large deviations of the time-averaged activity in the one-dimensional Fredrickson-Andersen model, both numerically and analytically. The model exhibits a dynamical phase transition, which appears as a singularity in the large deviation function. We analyze the finite-size scaling of this phase transition numerically, by generalizing an existing cloning algorithm to include a multicanonical feedback control: this significantly improves the computational efficiency. Motivated by these numerical results, we formulate an effective theory for the model in the vicinity of the phase transition, which accounts quantitatively for the observed behavior. We discuss potential applications of the numerical method and the effective theory in a range of more general contexts.
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Affiliation(s)
- Takahiro Nemoto
- Laboratoire de Probabilités et Modèles Aléatoires, Sorbonne Paris Cité, UMR 7599 CNRS, Université Paris Diderot, 75013 Paris, France
- Philippe Meyer Institute for Theoretical Physics, Physics Department, École Normale Supérieure & PSL Research University, 24 rue Lhomond, 75231 Paris Cedex 05, France
| | - Robert L Jack
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
| | - Vivien Lecomte
- Laboratoire de Probabilités et Modèles Aléatoires, Sorbonne Paris Cité, UMR 7599 CNRS, Université Paris Diderot, 75013 Paris, France
- LIPhy, Université Grenoble Alpes and CNRS, F-38042 Grenoble, France
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40
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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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41
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Shpielberg O, Don Y, Akkermans E. Numerical study of continuous and discontinuous dynamical phase transitions for boundary-driven systems. Phys Rev E 2017; 95:032137. [PMID: 28415355 DOI: 10.1103/physreve.95.032137] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2017] [Indexed: 06/07/2023]
Abstract
The existence and search for thermodynamic phase transitions is of unfading interest. In this paper, we present numerical evidence of dynamical phase transitions occurring in boundary-driven systems with a constrained integrated current. It is shown that certain models exhibit a discontinuous transition between two different density profiles and a continuous transition between a time-independent and a time-dependent profile. We also verified that the Kipnis-Marchioro-Presutti model exhibits no phase transitions in a range much larger than previously explored.
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Affiliation(s)
- Ohad Shpielberg
- Laboratoire de Physique Théorique, École Normale Supérieure and CNRS, 75005 Paris, France
- Physics Department, Technion-Israel Institute of Technology, 3200003 Haifa, Israel
| | - Yaroslav Don
- Physics Department, Technion-Israel Institute of Technology, 3200003 Haifa, Israel
| | - Eric Akkermans
- Physics Department, Technion-Israel Institute of Technology, 3200003 Haifa, Israel
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42
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Baek Y, Kafri Y, Lecomte V. Dynamical Symmetry Breaking and Phase Transitions in Driven Diffusive Systems. PHYSICAL REVIEW LETTERS 2017; 118:030604. [PMID: 28157352 DOI: 10.1103/physrevlett.118.030604] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2016] [Indexed: 06/06/2023]
Abstract
We study the probability distribution of a current flowing through a diffusive system connected to a pair of reservoirs at its two ends. Sufficient conditions for the occurrence of a host of possible phase transitions both in and out of equilibrium are derived. These transitions manifest themselves as singularities in the large deviation function, resulting in enhanced current fluctuations. Microscopic models which implement each of the scenarios are presented, with possible experimental realizations. Depending on the model, the singularity is associated either with a particle-hole symmetry breaking, which leads to a continuous transition, or in the absence of the symmetry with a first-order phase transition. An exact Landau theory which captures the different singular behaviors is derived.
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Affiliation(s)
- Yongjoo Baek
- Department of Physics, Technion, Haifa 32000, Israel
| | - Yariv Kafri
- Department of Physics, Technion, Haifa 32000, Israel
| | - Vivien Lecomte
- LIPhy, Université Grenoble Alpes and CNRS, F-38042 Grenoble, France
- Laboratoire Probabilités et Modèles Aléatoires, UMR7599 CNRS, Sorbonne Paris Cité, Université Pierre et Marie Curie and Université Paris Diderot, F-75013 Paris, France
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43
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Catanzaro MJ, Chernyak VY, Klein JR. Stochastic dynamics of extended objects in driven systems: I. Higher-dimensional currents in the continuous setting. Chem Phys 2016. [DOI: 10.1016/j.chemphys.2016.08.021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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44
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Abstract
We propose a simple diatomic system trapped inside an optical cavity to control the energy flow between two thermal baths. Through the action of the baths the system is driven to a non-equilibrium steady state. Using the Large Deviation theory we show that the number of photons flowing between the two baths is dramatically different depending on the symmetry of the atomic states. Here we present a deterministic scheme to prepare symmetric and antisymmetric atomic states with the use of external driving fields, thus implementing an atomic control switch for the energy flow.
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45
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Pérez-Espigares C, Garrido PL, Hurtado PI. Weak additivity principle for current statistics in d dimensions. Phys Rev E 2016; 93:040103. [PMID: 27176236 DOI: 10.1103/physreve.93.040103] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2015] [Indexed: 06/05/2023]
Abstract
The additivity principle (AP) allows one to compute the current distribution in many one-dimensional nonequilibrium systems. Here we extend this conjecture to general d-dimensional driven diffusive systems, and validate its predictions against both numerical simulations of rare events and microscopic exact calculations of three paradigmatic models of diffusive transport in d=2. Crucially, the existence of a structured current vector field at the fluctuating level, coupled to the local mobility, turns out to be essential to understand current statistics in d>1. We prove that, when compared to the straightforward extension of the AP to high d, the so-called weak AP always yields a better minimizer of the macroscopic fluctuation theory action for current statistics.
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Affiliation(s)
- C Pérez-Espigares
- University of Modena and Reggio Emilia, via G. Campi 213/b, 41125 Modena, Italy
| | - P L Garrido
- Institute Carlos I for Theoretical and Computational Physics and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, 18071 Granada, Spain
| | - P I Hurtado
- Institute Carlos I for Theoretical and Computational Physics and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, 18071 Granada, Spain
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46
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Lasanta A, Hurtado PI, Prados A. Statistics of the dissipated energy in driven diffusive systems. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2016; 39:35. [PMID: 27007607 DOI: 10.1140/epje/i2016-16035-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2015] [Accepted: 01/11/2016] [Indexed: 06/05/2023]
Abstract
Understanding the physics of non-equilibrium systems remains one of the major open questions in statistical physics. This problem can be partially handled by investigating macroscopic fluctuations of key magnitudes that characterise the non-equilibrium behaviour of the system of interest; their statistics, associated structures and microscopic origin. During the last years, some new general and powerful methods have appeared to delve into fluctuating behaviour that have drastically changed the way to address this problem in the realm of diffusive systems: macroscopic fluctuation theory (MFT) and a set of advanced computational techniques that make it possible to measure the probability of rare events. Notwithstanding, a satisfactory theory is still lacking in a particular case of intrinsically non-equilibrium systems, namely those in which energy is not conserved but dissipated continuously in the bulk of the system (e.g. granular media). In this work, we put forward the dissipated energy as a relevant quantity in this case and analyse in a pedagogical way its fluctuations, by making use of a suitable generalisation of macroscopic fluctuation theory to driven dissipative media.
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Affiliation(s)
- A Lasanta
- CNR-ISC and Dipartimento di Fisica, Università La Sapienza, p.le A. Moro 2, 00185, Rome, Italy.
| | - Pablo I Hurtado
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071, Granada, Spain
- Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, 18071, Granada, Spain
| | - A Prados
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080, Sevilla, Spain
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47
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Villavicencio-Sanchez R, Harris RJ. Local structure of current fluctuations in diffusive systems beyond one dimension. Phys Rev E 2016; 93:032134. [PMID: 27078319 DOI: 10.1103/physreve.93.032134] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2015] [Indexed: 06/05/2023]
Abstract
In order to illuminate the properties of current fluctuations in more than one dimension, we use a lattice-based Markov process driven into a nonequilibrium steady state. Specifically, we perform a detailed study of the particle current fluctuations in a two-dimensional zero-range process with open boundary conditions and probe the influence of the underlying geometry by comparing results from a square and a triangular lattice. Moreover, we examine the structure of local currents corresponding to a given global current fluctuation and comment on the role of spatial inhomogeneities for the discrepancies observed in testing some recent fluctuation symmetries.
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Affiliation(s)
- Rodrigo Villavicencio-Sanchez
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
- Dipartimento di Fisica "E. R. Caianiello," Università di Salerno, Via Giovanni Paolo II 132, 84084 Fisciano, Salerno, Italy
| | - Rosemary J Harris
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
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48
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del Pozo JJ, Garrido PL, Hurtado PI. Probing local equilibrium in nonequilibrium fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022117. [PMID: 26382354 DOI: 10.1103/physreve.92.022117] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2014] [Indexed: 06/05/2023]
Abstract
We use extensive computer simulations to probe local thermodynamic equilibrium (LTE) in a quintessential model fluid, the two-dimensional hard-disks system. We show that macroscopic LTE is a property much stronger than previously anticipated, even in the presence of important finite-size effects, revealing a remarkable bulk-boundary decoupling phenomenon in fluids out of equilibrium. This allows us to measure the fluid's equation of state in simulations far from equilibrium, with an excellent accuracy comparable to the best equilibrium simulations. Subtle corrections to LTE are found in the fluctuations of the total energy which strongly point to the nonlocality of the nonequilibrium potential governing the fluid's macroscopic behavior out of equilibrium.
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Affiliation(s)
- J J del Pozo
- Institute Carlos I for Theoretical and Computational Physics, and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, 18071 Granada, Spain
| | - P L Garrido
- Institute Carlos I for Theoretical and Computational Physics, and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, 18071 Granada, Spain
| | - P I Hurtado
- Institute Carlos I for Theoretical and Computational Physics, and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, 18071 Granada, Spain
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49
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50
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del Pozo JJ, Garrido PL, Hurtado PI. Scaling laws and bulk-boundary decoupling in heat flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:032116. [PMID: 25871063 DOI: 10.1103/physreve.91.032116] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2014] [Indexed: 06/04/2023]
Abstract
When driven out of equilibrium by a temperature gradient, fluids respond by developing a nontrivial, inhomogeneous structure according to the governing macroscopic laws. Here we show that such structure obeys strikingly simple scaling laws arbitrarily far from equilibrium, provided that both macroscopic local equilibrium and Fourier's law hold. Extensive simulations of hard disk fluids confirm the scaling laws even under strong temperature gradients, implying that Fourier's law remains valid in this highly nonlinear regime, with putative corrections absorbed into a nonlinear conductivity functional. In addition, our results show that the scaling laws are robust in the presence of strong finite-size effects, hinting at a subtle bulk-boundary decoupling mechanism which enforces the macroscopic laws on the bulk of the finite-sized fluid. This allows one to measure the marginal anomaly of the heat conductivity predicted for hard disks.
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Affiliation(s)
- Jesús J del Pozo
- Institute Carlos I for Theoretical and Computational Physics and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, 18071 Granada, Spain
| | - Pedro L Garrido
- Institute Carlos I for Theoretical and Computational Physics and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, 18071 Granada, Spain
| | - Pablo I Hurtado
- Institute Carlos I for Theoretical and Computational Physics and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, 18071 Granada, Spain
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