A mechanical model for Fourier's Law of heat conduction
David Ruelle

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.