Hamiltonian model of heat conductivity and Fourier law

TL;DR

This paper studies heat conduction in a one-dimensional particle system, demonstrating that Fourier's law holds with a temperature-dependent conductivity proportional to the square root of local temperature, and explores entropy aspects.

Contribution

It introduces a Hamiltonian model showing Fourier law with a specific temperature-dependent conductivity and analyzes entropy flux and production in nonequilibrium states.

Findings

Fourier law is satisfied in the model.

Thermal conductivity is proportional to √T(x).

Entropy flux and production are characterized.

Abstract

We investigate the stationary nonequilibrium states of a quasi one-dimensional system of heavy particles whose interaction is mediated by purely elastic collisions with light particles, in contact at the boundary with two heat baths with fixed temperatures $T^+$ and $T^-$. It is shown that Fourier law is satisfied with a thermal conductivity proportional to $\sqrt{T(x)}$ where $T(x)$ is the local temperature. Entropy flux and entropy production are also investigated.