Ergodic hypothesis

The Ergodic hypothesis (Ref 1 and 2) essentially states that an ensemble average (MC) of an observable, $<O>_{\mu }$ is equivalent to the time average, ${\overline {O}}_{T}$ of an observable (MD). i.e.

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \lim _{T\rightarrow \infty }{\overline {O}}_{T}(\{q_{0}(t)\},\{p_{0}(t)\})=<O>_{\mu }.}

A restatement of the ergodic hypothesis is to say that all allowed states are equally probable.

References

1. George D. Birkhoff, "Proof of the Ergodic Theorem", PNAS 17 pp. 656-660 (1931)
2. [LAS_1987_15_0263]