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.

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• How can we derive Fourier's Law from quantum mechanics? Exact master equation analysis
• Rectification of heat currents across nonlinear quantum chains: A versatile approach beyond weak thermal contact
• Pressure-induced recovery of Fourier's law in one dimensional momentum-conserving systems
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