Stochastic interacting particle systems out of equilibrium

TL;DR

This paper introduces stochastic lattice gas models out of equilibrium, highlighting a unified macroscopic picture and a variational approach linking thermodynamics and transport properties, with new theoretical insights.

Contribution

It presents a novel approach based on large fluctuations and Hamilton-Jacobi equations to connect non-equilibrium thermodynamics with transport coefficients.

Findings

Unified macroscopic description of out-of-equilibrium lattice gases

Development of a Hamilton-Jacobi type equation for non-equilibrium free energy

New theoretical insights into the relation between thermodynamics and transport

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.