A mechanism for the occurrence of irreversibility is proposed. It is based on the allowance for the relativistic factor in the mechanical system consisting of a finite number of particles interacting with one other particle in accordance with the law of elastic collision and moving in a vessel with a natural law of reflection from the vessel walls. The investigated model, a modification of Poincare model is the generalized billiard and describes the motion of three-dimensional gas from particles in a parallelepiped. It is proved that for general conditions the Gibbs entropy and thermodynamic entropy for this system of particles increase with time when the relativistic factor is taken into account, whereas in Newtonian case the Gibbs entropy is a constant.

generalized billiard, law of entropy increase

Mathematical modelling in actual problems of science and technics