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adj. Of or relating to certain systems that, given enough time, will eventually return to previously experienced state.

adj. Of or relating to a process in which every sequence or sample of sufficient size is equally representative of the whole.

adj. positive recurrent aperiodic state of stochastic systems; tending in probability to a limiting form that is independent of the initial conditions

"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."

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ergodic theory    ergodic hypothesis