Nonequilibrium gas and generalized billiards

The description of a nonequilibrium gas based on the notion of generalized billiards is proposed. Generalized billiards can be considered both in the framework of Newtonian mechanics and of the relativity theory. In the Newtonian case, for a generalized billiard inside a ball and the corresponding nonequilibrium gas the invariant measure is equivalent to the phase volume, and the Gibbs entropy are constructed. It is proved that the Gibbs entropy is constant and in the periodic case absolute values of particles velocities are bounded.