  This would make it plausible how Boltzmann could identify probabilities with relative times. But also, it would make it plausible that if a system starts out from a very small region (an improbable state) it will display a ‘tendency’ to evolve towards the overwhelmingly larger equilibrium state. Of course, this ‘tendency’ would have to be interpreted in a qualified sense: the same ergodic hypothesis would imply that the system cannot stay inside the equilibrium state forever and thus there would indeed be incessant fluctuations in and out of equilibrium. Indeed, one would have to state that the tendency to evolve from improbable to probable states is itself a probabilistic affair: as something that holds true for most of the initial states, or for most of the time, or as some type of expectation value or another. In short, we would then hopefully obtain some statistical version of the H-theorem. Exactly how this statistical H-theorem should be formulated remains an open problem in the Ehrenfests' point of view. Indeed they distinguish between several possible statistical interpretations of the theorem.