Fourier's Law from Closure Equations

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.

References in corpus (3)

• Self-Consistent Mode-Coupling Approach to 1D Heat Transport
• Energy Transport in Weakly Anharmonic Chains
• On the derivation of Fourier's law for coupled anharmonic oscillators

Cited by in corpus (3)

• Heat flux operator, current conservation and the formal Fourier's law
• Reconstructing Fourier's law from disorder in quantum wires
• Approach to equilibrium for the phonon Boltzmann equation