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arXiv · 1102.5488

A mechanical model for Fourier's law of heat conduction

David Ruelle
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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.

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David Ruelle. 2011-02-27. A mechanical model for Fourier's law of heat conduction. https://doi.org/10.1007/s00220-011-1304-z

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