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Hamiltonian model of heat conductivity and Fourier law

Christian Gruber·Annick Lesne
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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.

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Christian Gruber, Annick Lesne. 2004-10-16. Hamiltonian model of heat conductivity and Fourier law. https://doi.org/10.1016/j.physa.2004.12.022

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