Editing Ergodic hypothesis
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A restatement of the ergodic hypothesis is to say that all allowed states are equally probable. This holds true if | 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 | the ''metrical transitivity'' of general [[Hamiltonian]] systems holds true. | ||
==See also== | ==See also== | ||
*[[Fermi-Pasta-Ulam experiment]] | *[[Fermi-Pasta-Ulam experiment]] | ||
*[[Markov chain]] | *[[Markov chain]] | ||
*[[Mixing systems]] | *[[Mixing systems]] | ||
==References== | ==References== | ||
#[http://www.pnas.org/cgi/reprint/17/12/656 George D. Birkhoff, "Proof of the Ergodic Theorem", PNAS '''17''' pp. 656-660 (1931)] | |||
#[http://www.pnas.org/cgi/reprint/18/1/70 J. V. Neumann "Proof of the Quasi-ergodic Hypothesis", PNAS '''18''' pp. 70-82 (1932)] | |||
#[http://www.pnas.org/cgi/reprint/18/3/263 J. V. Neumann "Physical Applications of the Ergodic Hypothesis", PNAS '''18''' pp. 263-266 (1932)] | |||
#[http://www.pnas.org/cgi/reprint/18/3/279 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)) | |||
#[http://dx.doi.org/10.1070/RM1970v025n02ABEH003794 Ya G Sinai "Dynamical systems with elastic reflections", Russian Mathematical Surveys '''25''' pp. 137-189 (1970)] | |||
#[http://library.lanl.gov/cgi-bin/getfile?15-18.pdf Adrian Patrascioiu "The Ergodic-Hypothesis, A Complicated Problem in Mathematics and Physics", Los Alamos Science, '''15''' pp. 263- (1987)] | |||
#[http://dx.doi.org/10.1007/BF00384333 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) [http://iml.univ-mrs.fr/~lafont/rencontres/esi098.pdf (reprint)] | |||
[[category: Computer simulation techniques]] | [[category: Computer simulation techniques]] | ||