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Exponential convergence to non-equilibrium stationary states in classical statistical mechanics. (English) Zbl 0989.82023

Summary: We continue the study of a model for heat conduction [J.-P. Eckmann, C.-A. Pillet, and L. Rey-Bellet, Non-equilibrium statistical mechanics of anharmonic chains coupled to two heat baths at different temperatures, Commun. Math. Phys. 201, 657-697 (1999; Zbl 0932.60103)], consisting of a chain of nonlinear oscillators coupled to two Hamiltonian heat reservoirs at different temperatures. We establish existence of a Lyapunov 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.

MSC:

82C05 Classical dynamic and nonequilibrium statistical mechanics (general)

Citations:

Zbl 0932.60103
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