  We study the thermal rectification phenomenon in ``billiard'' systems with
interacting particles. This interaction induces a local dynamical response of
the billiard to an external thermodynamic gradient. To explain this dynamical
effect we study the steady state of an asymmetric billiard in terms of the
particle and energy reflection coefficients. This allows us to obtain
expressions for the region in parameter space where large thermal
rectifications are expected. Our results are confirmed by extensive numerical
simulations.
