Nonequilibrium steady states for a class of particle systems

This paper contains rigorous results on nonequilibrium steady states for a class of particle systems coupled to unequal heat baths. These stochastic models are derived from the mechanical chains studied by Eckmann and Young by randomizing certain quantities while retaining other features of the model. Our results include the existence and uniqueness of nonequilibrium steady states, their relation to Lebesgue measure, tail bounds on total energy and number of particles in the system, and exponential convergence to steady states from suitable initial conditions.