Existence of Nonequilibrium Steady State for a Simple Model of Heat Conduction.

This paper contains rigorous results for a simple stochastic model of heat conduction similar to the KMP (Knipnis-Marchiori-Presutti) model but with possibly energy-dependent interaction rates. We prove the existence and uniqueness of nonequilibrium steady states, their relation to Lebesgue measure, and exponential convergence to steady states from suitable initial conditions. [ABSTRACT FROM AUTHOR]