Stochastic interacting particle systems out of equilibrium
arXiv:0705.1247 · doi:10.1088/1742-5468/2007/07/P07014
Abstract
This paper provides an introduction to some stochastic models of lattice gases out of equilibrium and a discussion of results of various kinds obtained in recent years. Although these models are different in their microscopic features, a unified picture is emerging at the macroscopic level, applicable, in our view, to real phenomena where diffusion is the dominating physical mechanism. We rely mainly on an approach developed by the authors based on the study of dynamical large fluctuations in stationary states of open systems. The outcome of this approach is a theory connecting the non equilibrium thermodynamics to the transport coefficients via a variational principle. This leads ultimately to a functional derivative equation of Hamilton-Jacobi type for the non equilibrium free energy in which local thermodynamic variables are the independent arguments. In the first part of the paper we give a detailed introduction to the microscopic dynamics considered, while the second part, devoted to the macroscopic properties, illustrates many consequences of the Hamilton-Jacobi equation. In both parts several novelties are included.
36 pages
References in corpus (2)
Cited by in corpus (119)
- The large deviation approach to statistical mechanics
- Macroscopic fluctuation theory
- Nonequilibrium Markov processes conditioned on large deviations
- A pedestrian's view on interacting particle systems, KPZ universality, and random matrices
- Introduction to dynamical large deviations of Markov processes
- Current Fluctuations in One Dimensional Diffusive Systems with a Step Initial Density Profile
- Variational and optimal control representations of conditioned and driven processes
- Spontaneous Symmetry Breaking at the Fluctuating Level
- Large deviations for Markov processes with resetting
- Fluctuations of Current in Non-Stationary Diffusive Lattice Gases
- The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
- Dynamical symmetry breaking and phase transitions in driven diffusive systems
- Towards a nonequilibrium thermodynamics: a self-contained macroscopic description of driven diffusive systems
- Current large deviations for driven periodic diffusions
- A minimal model of dynamical phase transition
- Symmetries in Fluctuations Far from Equilibrium
- Duality for stochastic models of transport
- Dynamical phase transition for current statistics in a simple driven diffusive system
- Thermodynamics of currents in nonequilibrium diffusive systems: theory and simulation
- Test of the Additivity Principle for Current Fluctuations in a Model of Heat Conduction
- Large deviation approach to nonequilibrium systems
- A stochastic model of anomalous heat transport: analytical solution of the steady state
- Anomalous scaling of dynamical large deviations
- Clausius inequality and optimality of quasi static transformations for nonequilibrium stationary states
- Generic Dynamical Phase Transition in One-Dimensional Bulk-Driven Lattice Gases with Exclusion
- Current Fluctuations and Statistics During a Large Deviation Event in an Exactly-Solvable Transport Model
- Large Fluctuations in Driven Dissipative Media
- Long range correlations and phase transition in non-equilibrium diffusive systems
- Lagrangian phase transitions in nonequilibrium thermodynamic systems
- Current large deviations in a driven dissipative model
- Large deviation function of a tracer position in single file diffusion
- Convergence of large deviation estimators
- Large Fluctuations of the Macroscopic Current in Diffusive Systems: A Confirmation of the Additivity Principle
- On the Two Species Asymmetric Exclusion Process with Semi-Permeable Boundaries
- Nonlinear driven diffusive systems with dissipation: fluctuating hydrodynamics
- Extreme Current Fluctuations in Lattice Gases: Beyond Nonequilibrium Steady States
- Thermodynamic transformations of nonequilibrium states
- Bethe Ansatz for the Weakly Asymmetric Simple Exclusion Process and phase transition in the current distribution
- Dynamical properties of single-file diffusion
- Learning nonequilibrium control forces to characterize dynamical phase transitions
- Exact fluctuating hydrodynamics of active lattice gases -- Typical fluctuations
- Typical and rare fluctuations in nonlinear driven diffusive systems with dissipation
- Hydrodynamic limit of particle systems with long jumps
- A diffusive system driven by a battery or by a smoothly varying field
- Void formation in diffusive lattice gases
- Large deviations of currents in diffusions with reflective boundaries
- Optimal paths of non-equilibrium stochastic fields: the Kardar-Parisi-Zhang interface as a test case
- Numerical Study of Continuous and Discontinuous Dynamical Phase Transitions for Boundary Driven Systems
- Heat exchanges in a quenched ferromagnet
- Nonequilibrium Invariant Measure under Heat Flow
- Stationary non-equilibrium properties for a heat conduction model
- Dynamics of Repulsion Processes
- Entropy production in the non-equilibrium steady states of interacting many-body systems
- Phase fluctuations in the ABC model
- Weak additivity principle for current statistics in d-dimensions
- Duality relations in single-file diffusion
- Equilibrium states of a test particle coupled to finite size heat baths
- Anomalies, absence of local equilibrium and universality in 1-d particles systems
- Large deviations in the symmetric simple exclusion process with slow boundaries
- Boundary-induced instabilities in coupled oscillators
- A quasi-potential for conservation laws with boundary conditions
- Current fluctuations at a phase transition
- Dynamic fluctuations in unfrustrated systems: random walks, scalar fields and the Kosterlitz-Thouless phase
- Current fluctuations in an interacting active lattice gas
- Tricritical behavior in dynamical phase transitions
- Emergence of fluctuating traveling front solutions in macroscopic theory of noisy invasion fronts
- Generalized disorder averages and current fluctuations in run and tumble particles
- Action functional and quasi-potential for the Burgers equation in a bounded interval
- Compact Waves in Microscopic Nonlinear Diffusion
- Phase diagram of the ABC model with nonconserving processes
- Spatial fluctuation theorem
- Joint distribution of currents in the symmetric exclusion process
- A (2+1)-dimensional growth process with explicit stationary measures
- Optimality in self-organized molecular sorting
- Statistics of the dissipated energy in driven diffusive systems
- On Some Classes of Open Two-Species Exclusion Processes
- On the long range correlations of thermodynamic systems out of equilibrium
- Nonequilibrium Steady States for Certain Hamiltonian Models
- Molecular dynamics study of shear-induced long-range correlations in simple fluids
- An extension of Wiener integration with the use of operator theory
- Realm of Validity of the Crooks Relation
- Spectral signatures of symmetry-breaking dynamical phase transitions
- Probing local equilibrium in nonequilibrium fluids
- Exact Large Deviations of the Current in the Asymmetric Simple Exclusion Process with Open Boundaries
- Gibbsian stationary non equilibrium states
- Gradient structure and transport coefficients for strong particles
- Efficient large deviation estimation based on importance sampling
- Large deviation principles for nongradient weakly asymmetric stochastic lattice gases
- Exact time evolution formulae in the XXZ spin chain with domain wall initial state
- Entropy of stationary nonequilibrium measures of boundary driven symmetric simple exclusion processes
- Adaptive power method for estimating large deviations in Markov chains
- Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations
- Weak coupling limits in a stochastic model of heat conduction
- Perturbative large deviation analysis of non-equilibrium dynamics
- Scaling laws and bulk-boundary decoupling in heat flow
- On the Mean Residence Time in Stochastic Lattice-Gas Models
- Long range correlations in stochastic transport with energy and momentum conservation
- Current loops and fluctuations in the zero-range process on a diamond lattice
- Large deviations for correlated random variables described by a matrix product ansatz
- Heat conduction and the nonequilibrium stationary states of stochastic energy exchange processes
- A two-line representation of stationary measure for open TASEP
- Infinite family of universal profiles for heat current statistics in Fourier's law
- Nonequilibrium protection effect and spatial localization of noise-induced fluctuations: Quasi-one-dimensional driven lattice gas with partially penetrable obstacle
- 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
- Geometrical structures of the instantaneous current and their macroscopic effects: vortices and perspectives in non-gradient models
- The inclusion process: duality and correlation inequalities
- Stationary Distribution of open Asymmetric Simple Exclusion Processes on an Interval as a marginal of a two-layer ensemble
- Current fluctuations in finite-sized one-dimensional non-interacting passive and active systems
- Stationarity, time--reversal and fluctuation theory for a class of piecewise deterministic Markov processes
- Generic power laws in higher-dimensional lattice models with multidirectional hopping
- From combinatorics to large deviations for the invariant measures of some multiclass particle systems
- Microscopic and macroscopic perspectives on stationary nonequilibrium states
- Diffusion of energy in chains of oscillators with bulk noise
- Macroscopic dynamical fluctuations in Kac ring model
- Phase transition in the KMP model with Slow/Fast boundaries
- Effective Langevin equations leading to large deviation function of time-averaged velocity for a nonequilibrium Rayleigh piston
- State estimation of long-range correlated non-equilibrium systems: media estimation
- Dynamical large deviations for a boundary driven stochastic lattice gas model with many conserved quantities