A random dynamical system is said to be time-reversible if the sta- tistical properties of orbits do not change after reversing the arrow of time. The degree of irreversibility is captured by the notion of en- tropy production rate. A general formula for entropy production will be presented that applies to a class of thermal perturbations of bil- liard systems, for which it is meaningful to talk about energy exchange between billiard particle and boundary. This formula establishes a re- lation between the purely mathematical concept of entropy production rate and the physical concept of thermodynamic entropy. In particular, it recovers Clausius formulation of the second law of thermodynamics: the system must evolve so as to transfer energy from hot to cold. Fur- ther connections with stochastic thermodynamics will be illustrated with examples of simple "billiard thermal engines." This is joint work with Tim Chumley.