Thermodynamics of dispersing Billiards with Time-Dependent Boundaries

By means of a thermodynamic approach we analyze billiards in the form of the Lorentz gas with the open horizon. For periodic and stochastic oscillations of the scatterers, the average velocity of the particle ensemble as a function of time is analytically obtained. It is shown that the consequence of such oscillations is Fermi acceleration which is larger for periodic oscillations. The described results do not depend on the size of scatterers and their position. Only the property of the horizon openness is necessary. It is found that the developed thermodynamic approach is in a very good agreement with the results of the direct numerical simulations at which the corresponding billiard map is used.