Thermostatting by deterministic scattering

We present a mechanism for thermalizing a moving particle by microscopic deterministic scattering. As an example, we consider the periodic Lorentz gas. We modify the collision rules by including energy transfer between particle and scatterer such that the scatterer mimics a thermal reservoir with arbitrarily many degrees of freedom. The complete system is deterministic, time-reversible, and provides a microcanonical density in equilibrium. In the limit of the disk representing infinitely many degrees of freedom and by applying an electric field the system goes into a nonequilibrium steady state.