Abstract

The distinction between reversible and irreversible systems is usually made by examining whether the “equations of motion” are invariant or otherwise under time reversal. We consider here instead a criterion in terms of the time-dependence of the spontaneous fluctuations of the system. This leads us subsequently to consider the physical significance of the usual quantum modifications of the Brownian Movement formulae, and we are led to suggest that there are rather fundamental difficulties in dealing with simple irreversible systems when hf > kT. In particular we suggest that an irreversible description in terms of viscosity, friction, etc. in a thermal environment can only be valid over long enough time intervals, t, such that at least t å{h̵}/{kT}.