Existence and uniqueness of nonequilibrium stationary solutions in discrete thermostatted models

Abstract

This paper deals with the mathematical proof of the existence of the nonequilibrium stationary states in complex systems subjected to external force fields. Specifically the complex system is modeled within the recently proposed framework of the thermostatted kinetic theory. As the main result shows, the thermostat term allows the existence of the nonequilibrium stationary solutions, however a lower bound on the magnitude of the force field is required in order to ensure its uniqueness. The main result is gained by fixed point arguments.