  We present a novel mechanism for thermalizing a system of particles in
equilibrium and nonequilibrium situations, based on specifically modeling
energy transfer at the boundaries via a microscopic collision process. We apply
our method to the periodic Lorentz gas, where a point particle moves
diffusively through an ensemble of hard disks arranged on a triangular lattice.
First, collision rules are defined for this system in thermal equilibrium. They
determine the velocity of the moving particle such that the system is
deterministic, time reversible, and microcanonical. These collision rules can
systematically be adapted to the case where one associates arbitrarily many
degrees of freedom to the disk, which here acts as a boundary. Subsequently,
the system is investigated in nonequilibrium situations by applying an external
field. We show that in the limit where the disk is endowed by infinitely many
degrees of freedom it acts as a thermal reservoir yielding a well-defined
nonequilibrium steady state. The characteristic properties of this state, as
obtained from computer simulations, are finally compared to the ones of the
so-called Gaussian thermostated driven Lorentz gas.
