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

Mathematical Physics 2009-11-07 v1 math.MP Probability

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.

Keywords

Cite

@article{arxiv.math-ph/0110024,
  title  = {Exponential Convergence to Non-Equilibrium Stationary States in Classical Statistical Mechanics},
  author = {Luc Rey-Bellet and Lawrence E. Thomas},
  journal= {arXiv preprint arXiv:math-ph/0110024},
  year   = {2009}
}

Comments

To be published in Commun. Math. Phys