Exponential Convergence to Non-Equilibrium Stationary States in Classical Statistical Mechanics

Details Exponential Convergence to Non-Equilibrium Stationary States in Classical Statistical Mechanics Exponential Convergence to Non-Equilibrium Stationary States in Classical Statistical Mechanics

2001-10-20

arxiv.org/abs/math-ph/0110024v1

Physics

Mathematical Physics

To be published in Commun. Math. Phys

Scientific paper

10.1007/s002200100583

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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