Mixing systems - Revision history

Carl McBride: Added disambiguation

2008-07-30T10:29:10Z

Added disambiguation

← Older revision		Revision as of 12:29, 30 July 2008
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	~~{{stub-general}}~~		:''This article is about ergodic theory. For multicomponent systems see [[Mixtures]]''

	Systems that '''mix''' have a tendency over the course of time to head towards a state of statistical equilibrium. Mixing implies [[Ergodic hypothesis \| ergodicity]]. In 1963 (Ref. 3) Sinai outlined a proof that a system of <math>N</math> [[hard sphere model\| hard spheres]] enclosed within a cube which has perfectly reflecting walls		Systems that '''mix''' have a tendency over the course of time to head towards a state of statistical equilibrium. Mixing implies [[Ergodic hypothesis \| ergodicity]]. In 1963 (Ref. 3) Sinai outlined a proof that a system of <math>N</math> [[hard sphere model\| hard spheres]] enclosed within a cube which has perfectly reflecting walls
	is ergodic and mixing.		is ergodic and mixing.

Carl McBride: Added a little more

2008-07-29T10:52:40Z

Added a little more

← Older revision		Revision as of 12:52, 29 July 2008
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	{{stub-general}}		{{stub-general}}
	Systems that '''mix''' have a tendency over the course of time to head towards a state of statistical equilibrium. Mixing implies [[Ergodic hypothesis \| ergodicity]].		Systems that '''mix''' have a tendency over the course of time to head towards a state of statistical equilibrium. Mixing implies [[Ergodic hypothesis \| ergodicity]]. In 1963 (Ref. 3) Sinai outlined a proof that a system of <math>N</math> [[hard sphere model\| hard spheres]] enclosed within a cube which has perfectly reflecting walls
			is ergodic and mixing.
	==References==		==References==
	#[http://www.pnas.org/content/18/2/204.full.pdf+html Eberhard Hopf "Complete Transitivity and the Ergodic Principle", PNAS '''18''' pp. 204-209 (1932)]		#[http://www.pnas.org/content/18/2/204.full.pdf+html Eberhard Hopf "Complete Transitivity and the Ergodic Principle", PNAS '''18''' pp. 204-209 (1932)]
	#[http://www.pnas.org/content/18/3/255.full.pdf+html B. O. Koopman and J. v. Neumann "Dynamical Systems of Continuous Spectra", PNAS '''18''' pp. 255-263 (1932)]		#[http://www.pnas.org/content/18/3/255.full.pdf+html B. O. Koopman and J. v. Neumann "Dynamical Systems of Continuous Spectra", PNAS '''18''' pp. 255-263 (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))
	[[category: statistical mechanics]]		[[category: statistical mechanics]]

Carl McBride: A first save

2008-07-29T10:40:49Z

A first save

New page

{{stub-general}}
Systems that '''mix''' have a tendency over the course of time to head towards a state of statistical equilibrium. Mixing implies [[Ergodic hypothesis | ergodicity]].
==References==
#[http://www.pnas.org/content/18/2/204.full.pdf+html Eberhard Hopf "Complete Transitivity and the Ergodic Principle", PNAS '''18''' pp. 204-209 (1932)]
#[http://www.pnas.org/content/18/3/255.full.pdf+html B. O. Koopman and J. v. Neumann "Dynamical Systems of Continuous Spectra", PNAS '''18''' pp. 255-263 (1932)]
[[category: statistical mechanics]]