Large deviation approach to non equilibrium processes in stochastic lattice gases

@article{Bertini2006LargeDA,
  title={Large deviation approach to non equilibrium processes in stochastic lattice gases},
  author={Lorenzo Bertini and Alberto De Sole and Davide Gabrielli and Giovanni Jona-Lasinio and Claudio Landim},
  journal={Bulletin of the Brazilian Mathematical Society},
  year={2006},
  volume={37},
  pages={611-643}
}
Abstract.We present a review of recent work on the statistical mechanics of non equilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and can be studied rigorously providing a source of challenging mathematical problems. In this way, some principles of wide validity have been obtained leading to interesting physical consequences. 

Macroscopic fluctuation theory

Stationary non-equilibrium states describe steady flows through macroscopic systems. Although they represent the simplest generalization of equilibrium states, they exhibit a variety of new

Hydrodynamic Limit for a Boundary Driven Stochastic Lattice Gas Model with Many Conserved Quantities

We prove the hydrodynamic limit for a particle system in which particles may have different velocities. We assume that we have two infinite reservoirs of particles at the boundary: this is the

Hydrodynamic behavior of boundary driven stochastic lattice gas models and interacting particle systems with conductances in random environments

We prove the hydrodynamic limit for a particle system in which particles may have different velocities. We assume that we have two infinite reservoirs of particles on the boundary: this is the

Microscopic versus macroscopic approaches to non-equilibrium systems

The one-dimensional symmetric simple exclusion process (SSEP) is one of the very few exactly soluble models of non-equilibrium statistical physics. It describes a system of particles which diffuse

Fluctuation Relations in Stochastic Thermodynamics

Fluctuation relations are identities, holding in non-equilibrium systems, that have attracted a lot of interest in the last 20 years. This is a series of 4 lectures discussing various aspects of such

Dynamical large deviations for the boundary driven weakly asymmetric exclusion process

We consider the weakly asymmetric exclusion process on a bounded interval with particle reservoirs at the endpoints. The hydrodynamic limit for the empirical density, obtained in the diffusive

Stochastic interacting particle systems out of equilibrium

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

Large deviations of the empirical current for the boundary driven Kawasaki process with long range interaction

We consider a lattice gas evolving in a bounded cylinder of length 2N+1 and interacting via a Neuman Kac interaction of range N, in contact with particles reservoirs at dierent densities. We

Fluctuation theorems for stochastic dynamics

Fluctuation theorems make use of time reversal to make predictions about entropy production in many-body systems far from thermal equilibrium. Here we review the wide variety of distinct, but

Dynamical fluctuations for semi-Markov processes

We develop an Onsager–Machlup-type theory for nonequilibrium semi-Markov processes. Our main result is an exact large-time asymptotics for the joint probability of the occupation times and the

References

SHOWING 1-10 OF 30 REFERENCES

Current fluctuations in stochastic lattice gases.

A large deviation theory is established for the space-time fluctuations of the empirical current for lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles.

Large deviations of the empirical current in interacting particle systems

We study current fluctuations in lattice gases in the hydrodynamic scaling limit. More precisely, we prove a large deviation principle for the empirical current in the symmetric simple exclusion

Lattice gas models in contact with stochastic reservoirs: Local equilibrium and relaxation to the steady state

Extending the results of a previous work, we consider a class of discrete lattice gas models in a finite interval whose bulk dynamics consists of stochastic exchanges which conserve the particle

Large Deviations for the Boundary Driven Symmetric Simple Exclusion Process

The large deviation properties of equilibrium (reversible) lattice gases are mathematically reasonably well understood. Much less is known in nonequilibrium, namely for nonreversible systems. In this

Non Equilibrium Current Fluctuations in Stochastic Lattice Gases

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large

Fluctuations in stationary nonequilibrium states of irreversible processes.

We formulate a dynamical fluctuation theory for stationary nonequilibrium states (SNS) which covers situations in a nonlinear hydrodynamic regime and is verified explicitly in stochastic models of

From dynamic to static large deviations in boundary driven exclusion particle systems

Fluctuations and Irreversible Processes

The probability of a given succession of (nonequilibrium) states of a spontaneously fluctuating thermodynamic system is calculated, on the assumption that the macroscopic variables defining a state

Distribution of current in nonequilibrium diffusive systems and phase transitions.

This time dependent profile persists in the large drift limit and allows one to understand on physical grounds the results obtained earlier for the totally asymmetric exclusion process on a ring.

Hydrodynamics of stationary non-equilibrium states for some stochastic lattice gas models

We consider discrete lattice gas models in a finite interval with stochastic jump dynamics in the interior, which conserve the particle number, and with stochastic dynamics at the boundaries chosen