Abstract

We continue the study of a model for heat conduction [6] consisting of a chain of non-linear oscillators coupled to two Hamiltonian heat reservoirs at dierent temperatures. We establish existence of a Liapunov function for the chain dynamics and use it to show exponentially fast convergence of the dynamics to a unique stationary state. Ingredients of the proof are the reduction of the innite dimensional dynamics to a nite-dimensional stochastic process as well as a bound on the propagation of energy in chains of anharmonic oscillators. 1 Introduction In its present state, non-equilibrium statistical mechanics is lacking the rm theoretical foundations that equilibrium statistical mechanics has. This is due, perhaps, to the extremely great variety of physical phenomena that non-equilibrium statistical mechanics describes. We will concentrate here on a system which is maintained, by suitable forces, in a state far from equilibrium. In such an idealization, the non-equilibrium phenome...

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