A Model of Heat Conduction

TL;DR

This paper introduces a deterministic scattering model for heat conduction that is continuous in space and demonstrates the existence of a unique non-equilibrium steady state under stochastic boundary conditions close to Maxwellians.

Contribution

It presents a novel scattering model for heat conduction with a proof of a unique steady state under specific boundary conditions.

Findings

Existence of a unique non-equilibrium steady state

Model is continuous in space with Boltzmann-like features

Steady state established under near-Maxwellian boundary conditions

Abstract

We define a deterministic ``scattering'' model for heat conduction which is continuous in space, and which has a Boltzmann type flavor, obtained by a closure based on memory loss between collisions. We prove that this model has, for stochastic driving forces at the boundary, close to Maxwellians, a unique non-equilibrium steady state.