01-98 Luc Rey-Bellet and Lawrence E. Thomas

Exponential convergence to non-equilibrium stationary states in classical statistical mechanics (324K, Postscript) Mar 9, 01

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Abstract. We continue the study of a model for heat conduction consisting of a chain of non-linear oscillators coupled to two Hamiltonian heat reservoirs at different 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 infinite dimensional dynamics to a finite-dimensional stochastic process as well as a bound on the propagation of energy in chains of anharmonic oscillators.

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