Almost Periodicity and the Quantal H Theorem

It is proved that the H theorem for an ensemble of isolated quantal systems with a discrete energy spectrum is false provided the systems satisfy certain broad conditions: the theorem is false for bounded many-particle systems with potential interaction, provided that interaction contains no repulsive singularities stronger than r−2 and no attractive singularities stronger than r−1. Ensembles of such systems behave almost periodically, in the sense of H. Bohr. The entropy and the probability of finding an observable in a given range are both almost periodic functions of time.