A mechanical model for Fourier's law for heat conduction
A mechanical model for Fourier's law for heat conduction

D. Ruelle, L'Institut des Hautes Études Scientifiques (IHÉS)
Fine Hall 224
Nonequilibrium statistical mechanics close to equilibrium is a physically satisfactory theory centered on the linear response formula of GreenKubo. 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 heatconducting 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.