# Ergodic hypothesis

The **Ergodic hypothesis** essentially states that an ensemble average (i.e. an instance of a Monte Carlo simulation) of an observable, is equivalent to the time average, of an observable (i.e. molecular dynamics). *i.e.*

A restatement of the ergodic hypothesis is to say that all allowed states are equally probable. This holds true if
the *metrical transitivity* of general Hamiltonian systems holds true. Recent experiments have demonstrated the hypothesis ^{[1]}.

## See also[edit]

## References[edit]

- Related reading

- George D. Birkhoff, "Proof of the Ergodic Theorem", PNAS
**17**pp. 656-660 (1931) - J. V. Neumann "Proof of the Quasi-ergodic Hypothesis", PNAS
**18**pp. 70-82 (1932) - J. V. Neumann "Physical Applications of the Ergodic Hypothesis", PNAS
**18**pp. 263-266 (1932) - G. D. Birkhoff and B. O. Koopman "Recent Contributions to the Ergodic Theory", PNAS
**18**pp. 279-282 (1932) - Ya. G. Sinai "On the Foundation of the Ergodic Hypothesis for a Dynamical System of Statistical Mechanics", Doklady Akademii Nauk SSSR
**153**pp. 1261–1264 (1963) (English version: Soviet Math. Doklady**4**pp. 1818-1822 (1963)) - Ya G Sinai "Dynamical systems with elastic reflections", Russian Mathematical Surveys
**25**pp. 137-189 (1970) - Adrian Patrascioiu "The Ergodic-Hypothesis, A Complicated Problem in Mathematics and Physics", Los Alamos Science,
**15**pp. 263- (1987) - Jan von Plato "Boltzmann's ergodic hypothesis", Archive for History of Exact Sciences
**42**pp. 71-89 (1991) - Domokos Ssász "Boltzmann's Ergodic Hypothesis, a Conjecture for Centuries?", Studia Scientiarum Mathematicarum Hungarica
**31**pp. 299-322 (1996) (reprint)