The other time paradox was used against a colleague. Loschmidt tried to find arguments against Boltzmann´s ergodic hypothesis.

According to the second law of thermodynamics, the entropy in a system of many particles grows spontaneously. A decrease of entropy must be explained by an external force.

According to the physical axioms the time is reversible and all processes can run backwards if time were inversed. In a system of many particles a such time inversion should lead to the decrease of entropy. This seems to be a paradox. But according to the definition, a process decreasing of entropy is not a spontaneous one. Therefore even the time inversion as not a spontaneous process. Till now no spontaneous time inversion was observed in whole thermodynamical systems and an invention of a time machine is comparable with an invention of the perpetuum mobile.

There exists another time paradox, the Zermelo- Poincaré return paradox. According to it all systems must return into their original state within a finite time.

This demand can be interpreted as an impossibility of an infinite time existence of a system of finite size.

References

1. J. E. Mayer, M. Goeppert Mayer, Statistical Mechanics, Wiley, New York, 1978.

2. J. W. Zwanzinger, A. Pines, Topological invariants in Fermi systems with Time-reversal invariance, Chemtracs Anal. Phys. Chem., 1989, 1, 339-341.