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