Local equilibrium in inhomogeneous stochastic models of heat transport

TL;DR

This paper extends duality methods to inhomogeneous lattice gas models, proving local equilibrium in hydrodynamic limits and steady states for systems with spatially varying properties.

Contribution

It introduces a generalized duality framework for inhomogeneous systems and applies it to establish local equilibrium results in complex heat transport models.

Findings

Proved local equilibrium in high-dimensional inhomogeneous systems.

Established nonequilibrium steady states in one-dimensional inhomogeneous systems.

Extended duality techniques to models with spatially varying interaction rates.

Abstract

We extend the duality of Kipnis Marchioro and Presutti to inhomogeneous lattice gas systems where either the components have different degrees of freedom or the rate of interaction depends on the spatial location. Then the dual process is applied to prove local equilibrium in the hydrodynamic limit for some inhomogeneous high dimensional systems andin the nonequilibrium steady state for one dimensional systems with arbitrary inhomogeneity.