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

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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 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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Received: 12 March 2001 / Accepted: 5 August 2001

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Rey-Bellet, L., Thomas, L. Exponential Convergence to Non-Equilibrium Stationary States in Classical Statistical Mechanics. Commun. Math. Phys. 225, 305–329 (2002). https://doi.org/10.1007/s002200100583

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  • DOI: https://doi.org/10.1007/s002200100583

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