Stochastic interacting particle systems out of equilibrium

TLDR

A unified macroscopic picture is emerging for lattice gas models, despite microscopic differences, and is relevant to diffusion‑dominated phenomena. The paper introduces stochastic lattice gas models out of equilibrium and reviews recent results. The authors use a dynamical large‑fluctuation approach to derive a variational principle linking non‑equilibrium thermodynamics and transport coefficients, yielding a Hamilton–Jacobi functional‑derivative equation for the free energy. The work demonstrates many consequences of this Hamilton–Jacobi equation and presents several novel results.

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.