A mechanical model for Fourier's law of heat conduction

TL;DR

This paper introduces a deterministic mechanical model of a heat-conducting chain that allows for a rigorous derivation of Fourier's law, addressing a longstanding theoretical challenge.

Contribution

It presents a novel mechanical model where Fourier's law can be rigorously derived, advancing the theoretical understanding of heat conduction.

Findings

Rigorous derivation of Fourier's law from mechanics

Model removes kinetic energy fluctuations at nodes

Addresses a major unsolved problem in heat conduction theory

Abstract

Nonequilibrium statistical mechanics close to equilibrium is a physically satisfactory theory centered on the linear response formula of Green-Kubo. This formula results from a formal first order perturbation calculation without rigorous justification. A rigorous derivation of Fourier's law for heat conduction from the laws of mechanics remains thus a major unsolved problem. In this note we present a deterministic mechanical model of a heat-conducting chain with nontrivial interactions, where kinetic energy fluctuations at the nodes of the chain are removed. In this model the derivation of Fourier's law can proceed rigorously.