# Heat conduction and the nonequilibrium stationary states of stochastic energy exchange processes

## TL;DR

This paper provides a systematic analysis of non-equilibrium stationary states in a solvable heat conduction model, deriving Fourier's law and correlations without dual process analysis, and extends results to generalized gradient models.

## Contribution

It offers a new systematic characterization of non-equilibrium states in the KMP model and its generalizations, avoiding dual process analysis.

## Key findings

- Derivation of Fourier's law in the model
- Explicit static correlations and covariance matrices
- Extension to generalized gradient models

## Abstract

I revisit the exactly solvable Kipnis--Marchioro--Presutti model of heat conduction [J. Stat. Phys. 27 65 (1982)] and describe, for one-dimensional systems of arbitrary sizes whose ends are in contact with thermal baths at different temperatures, a systematic characterization of their non-equilibrium stationary states. These arguments avoid resorting to the analysis of a dual process and yield a straightforward derivation of Fourier's law, as well as higher-order static correlations, such as the covariant matrix. The transposition of these results to families of gradient models generalizing the KMP model is established and specific cases are examined.