Free Energy Functional for Nonequilibrium Systems: An Exactly Solvable Case

Abstract

We consider the steady state of an open system in which there is a flux of matter between two reservoirs at different chemical potentials. For a large system of size $N$, the probability of any macroscopic density profile $\rho (x)$ is $\exp [-N\mathcal{F}(\{\rho \})]$; $\mathcal{F}$ thus generalizes to nonequilibrium systems the notion of free energy density for equilibrium systems. Our exact expression for $\mathcal{F}$ is a nonlocal functional of $\rho$, which yields the macroscopically long range correlations in the nonequilibrium steady state previously predicted by fluctuating hydrodynamics and observed experimentally.

4 pages, RevTeX. Changes: correct minor errors, add reference, minor rewriting requested by editors and referee

References in corpus (1)

• Fluctuations in Stationary non Equilibrium States

Cited by in corpus (130)

• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Macroscopic fluctuation theory
• Current fluctuations in non-equilibrium diffusive systems: an additivity principle
• The Totally Asymmetric Simple Exclusion Process with Langmuir Kinetics
• Distribution of current in non-equilibrium diffusive systems and phase transitions
• Large Deviation of the Density Profile in the Steady State of the Open Symmetric Simple Exclusion Process
• Stochastic interacting particle systems out of equilibrium
• Non equilibrium current fluctuations in stochastic lattice gases
• Universal cumulants of the current in diffusive systems on a ring
• Current fluctuations in the one dimensional Symmetric Exclusion Process with open boundaries
• Current Fluctuations in One Dimensional Diffusive Systems with a Step Initial Density Profile
• Exact Free Energy Functional for a Driven Diffusive Open Stationary Nonequilibrium System
• Mapping out of equilibrium into equilibrium in one-dimensional transport models
• Current fluctuations in the zero-range process with open boundaries
• Cumulants and large deviations of the current through non-equilibrium steady states
• Large deviation functional of the weakly asymmetric exclusion process
• Large deviations for a stochastic model of heat flow
• Solvable quantum nonequilibrium model exhibiting a phase transition and a matrix product representation
• Fluctuations of Current in Non-Stationary Diffusive Lattice Gases
• Non-equilibrium two-phase coexistence in a confined granular layer
• Resolving Discrepancy between Liouvillian Gap and Relaxation Time in Boundary-Dissipated Quantum Many-Body Systems
• Microscopic versus macroscopic approaches to non-equilibrium systems
• Exact solution of the macroscopic fluctuation theory for the symmetric exclusion process
• Fluctuations in ballistic transport from Euler hydrodynamics
• Large deviations for the boundary driven symmetric simple exclusion process
• The asymmetric Exclusion Process and Brownian Excursions
• Transport fluctuations in integrable models out of equilibrium
• Dynamics of interacting particle systems: stochastic process and field theory
• Phase Transition in the ABC Model
• Exact large-deviation statistics for a nonequilibrium quantum spin chain
• Mapping Nonequilibrium onto Equilibrium: The Macroscopic Fluctuations of Simple Transport Models
• Constraint driven condensation in large fluctuations of linear statistics
• The race to the bottom: approaching the ideal glass?
• Large deviation approach to nonequilibrium systems
• Singularities in large deviation functions
• Entropy of Open Lattice Systems
• Thermodynamic Limit for the Mallows Model on $S_n$
• Ballistic macroscopic fluctuation theory
• Large deviation approach to non equilibrium processes in stochastic lattice gases
• Relaxation times in the ASEP model using a DMRG method
• Time-reversal symmetry and fluctuation relations in non-equilibrium quantum steady states
• Lagrangian phase transitions in nonequilibrium thermodynamic systems
• Minimum dissipation principle in stationary non equilibrium states
• Large-deviation statistics of a diffusive quantum spin chain and the additivity principle
• Brownian motion: a paradigm of soft matter and biological physics
• Nonequilibrium Dynamics in Low Dimensional Systems
• Entropic Fluctuations in Statistical Mechanics I. Classical Dynamical Systems
• Dynamic correlation functions and Boltzmann Langevin approach for driven one dimensional lattice gas
• Entropy and Nonlinear Nonequilibrium Thermodynamic Relation for Heat Conducting Steady States
• Large deviations conditioned on large deviations II: Fluctuating hydrodynamics
• Continuum Free-Energy formulation for a class of Lattice Boltzmann multiphase models
• Current fluctuations of interacting active Brownian particles
• Computation of current cumulants for small nonequilibrium systems
• Equilibrium-like fluctuations in some boundary-driven open diffusive systems
• Twenty five years after KLS: A celebration of non-equilibrium statistical mechanics
• Eulerian and Lagrangian pictures of non-equilibrium diffusions
• Matrix Ansatz for the Fluctuations of the Current in the ASEP with Open Boundaries
• Statistics of Entropy Production in Linearized Stochastic System
• Nonequilibrium stationary states and equilibrium models with long range interactions
• Nonequilibrium Steady State Driven by a Nonlinear Drift Force
• Some exact results for the trapping of subdiffusive particles in one dimension
• Condensation transition in joint large deviations of linear statistics
• Disordered exclusion process revisited: some exact results in the low-current regime
• Finite-Size Scaling in the Driven Lattice Gas
• Duality and hidden equilibrium in transport models
• Arrhenius law for interacting diffusive systems
• An equilibrium state with macroscopic correlations
• Exact equalities and thermodynamic relations for nonequilibrium steady states
• Autonomous Brownian gyrators: a study on gyrating characteristics
• Mesoscopic Full Counting Statistics and Exclusion models
• Can the Macroscopic Fluctuation Theory be Quantized?
• Nanoscale correlated disorder in out-of-equilibrium myelin ultrastructure
• Asymmetric Simple Exclusion Process with open boundaries and Quadratic Harnesses
• Exact solution to integrable open multi-species SSEP and macroscopic fluctuation theory
• Exact Large Deviation Functional of a Stationary Open Driven Diffusive System: The Asymmetric Exclusion Process
• Large deviations in weakly interacting boundary driven lattice gases
• Totally asymmetric exclusion process with long-range hopping
• Stationary correlations for a far-from-equilibrium spin chain
• Integrable Floquet dynamics, generalized exclusion processes and "fused" matrix ansatz
• Linear response theory in stochastic many-body systems revisited
• Dissipation-driven integrable fermionic systems: from graded Yangians to exact nonequilibrium steady states
• Exact solution of an integrable non-equilibrium particle system
• Large deviations in the symmetric simple exclusion process with slow boundaries
• Phase transitions in nonequilibrium d-dimensional models with q absorbing states
• Generalized disorder averages and current fluctuations in run and tumble particles
• Additivity, density fluctuations, and nonequilibrium thermodynamics for active Brownian particles
• Theoretical approaches to the steady-state statistical physics of interacting dissipative units
• Non-equilibrium stationary state of a two-temperature spin chain
• The kinetic exclusion process: a tale of two fields
• Unique extension of the maximum entropy principle to phase coexistence in heat conduction
• A fluctuation-response relation of many Brownian particles under non-equilibrium conditions
• Bernoulli variables, classical exclusion processes and free probability
• Nonequilibrium fluctuations in small systems: From physics to biology
• Shot-noise statistics in diffusive conductors
• Slow Kinetics of Brownian Maxima
• Spectral signatures of symmetry-breaking dynamical phase transitions
• Integrability in the weak noise theory
• Energy Profile Fluctuations in Dissipative Nonequilibrium Stationary States
• Probing local equilibrium in nonequilibrium fluids
• Spatial correlations, additivity and fluctuations in conserved-mass transport processes
• A note on Fick's law with phase transitions
• Stationary nonequilibrium statistical mechanics
• Large deviations of density fluctuations in the boundary driven Quantum Symmetric Simple Inclusion Process
• Nonequilibrium Thermodynamics of the First and Second Kind: Averages and Fluctuations
• Large Deviations in the Symmetric Simple Exclusion Process with Slow Boundaries: A Hydrodynamic Perspective
• Thermodynamic Theory of Phase Transitions in Driven Lattice Gases
• Symmetric exclusion processes on a ring with moving defects
• Approach to a non-equilibrium steady state
• Current statistics in the q-boson zero range process
• Systematic derivation of coarse-grained fluctuating hydrodynamic equations for many Brownian particles under non-equilibrium condition
• A perturbation theory for large deviation functionals in fluctuating hydrodynamics
• Quantum Reciprocity Conjecture for the Non-Equilibrium Steady State
• Positional information trade-offs in boundary-driven reaction-diffusion systems
• Steady state thermodynamics
• Totally asymmetric limit for models of heat conduction
• Interacting Random Walkers and Non-Equilibrium Fluctuations
• Coupling independent walkers and the inclusion process
• Interface fluctuations in non equilibrium stationary states: the SOS approximation
• Generalized free energy and excess/housekeeping decomposition in nonequilibrium systems: from large deviations to thermodynamic speed limits
• Finite size corrections to the large deviation function of the density in the one dimensional symmetric simple exclusion process
• Lecture notes on large deviations in non-equilibrium diffusive systems
• Universal and non-universal signatures in the scaling functions of critical variables
• Understanding random-walk dynamical phase coexistence through waiting times
• Proper effective temperature and order parameters in relativistic non-equilibrium steady states
• Limits to positional information in boundary-driven systems
• Slow decay of dynamical correlation functions for nonequilibrium quantum states
• Quasi-potentials in the Nonequilibrium Stationary States or a method to get explicit solutions of Hamilton-Jacobi equations
• Generic power laws in higher-dimensional lattice models with multidirectional hopping