Duality and exact correlations for a model of heat conduction

TL;DR

This paper investigates a stochastic heat conduction model, deriving a dual process for correlation functions, revealing long-range correlations with current, and connecting it to the symmetric exclusion process.

Contribution

It introduces an exact dual particle process for the model's correlations and explores its long-range behavior and relation to exclusion processes.

Findings

Exact covariance expression shows long-range correlations with current.

Dual process describes evolution of all correlation functions.

Connection established with the simple symmetric exclusion process.

Abstract

We study a model of heat conduction with stochastic diffusion of energy. We obtain a dual particle process which describes the evolution of all the correlation functions. An exact expression for the covariance of the energy exhibits long-range correlations in the presence of a current. We discuss the formal connection of this model with the simple symmetric exclusion process.