Fourier's Law from Closure Equations
Jean Bricmont, Antti Kupiainen
TL;DR
This paper rigorously derives Fourier's law for a Hamiltonian system of coupled oscillators with heat baths, showing the proportionality of heat flux to temperature gradient and nonlinear temperature profiles.
Contribution
It provides a rigorous derivation of Fourier's law from closure equations in a nonequilibrium Hamiltonian oscillator system, including temperature-dependent conductivity.
Findings
Heat flux is proportional to the temperature gradient.
Stationary temperature profile is nonlinear.
Heat conductivity depends on temperature.
Abstract
We give a rigorous derivation of Fourier's law from a system of closure equations for a nonequilibrium stationary state of a Hamiltonian system of coupled oscillators subjected to heat baths on the boundary. The local heat flux is proportional to the temperature gradient with a temperature dependent heat conductivity and the stationary temperature exhibits a nonlinear profile.
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