  The Ehrenfests (1912) paper was the first to recognize these questions, and to provide a partial answer: Assuming a certain hypothesis of Boltzmann's, which they dubbed the ergodic hypothesis, they pointed out that for an isolated system the micro-canonical distribution is the unique stationary probability distribution. Hence, if one demands that an ensemble of isolated systems describing thermal equilibrium must be represented by a stationary distribution, the only choice for this purpose is the micro-canonical one. Similarly, they pointed out that under the ergodic hypothesis infinite time averages and ensemble averages were identical. This, then, would provide a desired link between the probabilities of the older kinetic gas theory and those of statistical mechanics, at least in equilibrium and in the infinite time limit. Yet the Ehrenfests simultaneously expressed strong doubts about the validity of the ergodic hypothesis. These doubts were soon substantiated when in 1913 Rozenthal and Plancherel proved that the hypothesis was untenable for realistic gas models.