Luc Rey-Bellet and Lawrence E. Thomas
Exponential convergence to non-equilibrium stationary states in 
classical statistical mechanics
(324K, Postscript)

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.