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.

$\underset{T\to \mathrm{\infty }}{lim}{\overline{O}}_T(\{q_0(t)\},\{p_0(t)\})=<O{>}_{\mu }.$

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]