Weak coupling limits in a stochastic model of heat conduction

TL;DR

This paper investigates the weak coupling limits in a stochastic heat conduction model, analyzing the non-equilibrium steady state and correlation functions for small systems to understand deviations from local equilibrium.

Contribution

It provides new insights into the behavior of the Brownian momentum process under weak coupling, including explicit correlation functions for small systems.

Findings

Two-point correlation functions are generally not multilinear.

The non-equilibrium steady state deviates from local equilibrium as coupling weakens.

Different weak coupling settings influence the steady state's properties.

Abstract

We study the Brownian momentum process, a model of heat conduction, weakly coupled to heat baths. In two different settings of weak coupling to the heat baths, we study the non-equilibrium steady state and its proximity to the local equilibrium measure in terms of the strength of coupling. For three and four site systems, we obtain the two-point correlation function and show it is generically not multilinear.