On the mechanism for the origin of irreversibility and unlimited energy growth in a model of statistical mechanics (Q1602638)

The system treated consists of \(N\) identical particles moving in a 1-dimensional vessel in the vertical direction. Particles interact according to the law of elastic collisions among themselves as well as with periodically forcing lower and upper walls. The author shows that for the Newtonian case the Gibbs phase space entropy oscillates in a restricted range and that the entropy of configuration space introduced by him is constant in time. But if particles move according to the laws of special relativity then both of the above-mentioned entropies increase with time indefinitely. In this case the energy of the particles also increases exponentially with time. Thus, taking into account relativistic influence, the origin of irreversibility can be understood in a qualitatively new way. But for a rigorous treatment the author should have shown that his system is ergodic. Also, subexpressions in equation (11) should be treated in a relativistic fashion. Let us note that the same phenomena were demonstrated even for the general relativistic case in [the reviewer, Nuovo Cimento B (11) 69, No. 1, 136--144 (1982)].