This nice expository article gives account of the Boltzmann’s ergodic hypothesis and gas model in terms of modern ergodic theory. Different planar billiards and their chaotic properties are discussed. The ergodic-theoretic history behind the formulation of the Boltzmann-Sinai ergodic conjecture is related, and the Sinai billiard model for hard balls gases is described. Basics from hyperbolicity and Pesin theory are reviewed with an eye on the ergodicity problem of semi-dispersing billiards. Finally, recent progress on the full Boltzmann-Sinai conjecture – still open – are summarized.
There is an excellent related survey by L.-S. Young in [Mazur, B. (ed.) et al., Current developments in mathematics, 1998, Proceedings of the conference, Cambridge, MA, USA, 1998, Somerville, MA: International Press, 237–278 (1999; Zbl 1003.37023)].