Ensembles in thermostatistics - Revision history

Carl McBride: /* See also */ Added an internal link

2011-01-12T13:45:53Z

Carl McBride: /* Representative ensembles */ Added an internal link to Isoenthalpic–isobaric ensemble

2008-08-04T10:26:48Z

Representative ensembles: Added an internal link to Isoenthalpic–isobaric ensemble

← Older revision		Revision as of 12:26, 4 August 2008
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	*[[Gibbs ensemble]]		*[[Gibbs ensemble]]
	*[[Grand canonical ensemble]] (<math>\mu VT</math>)		*[[Grand canonical ensemble]] (<math>\mu VT</math>)
			*[[Isoenthalpic–isobaric ensemble]] (<math>NpH</math>)
	*[[Isothermal-isobaric ensemble]] (<math>NpT</math>)		*[[Isothermal-isobaric ensemble]] (<math>NpT</math>)
	*[[Microcanonical ensemble]] (<math>NVE</math>)		*[[Microcanonical ensemble]] (<math>NVE</math>)

	==See also==		==See also==
	*[[Gibbs ensemble Monte Carlo]]		*[[Gibbs ensemble Monte Carlo]]

Carl McBride: /* References */ Added external links to scanned images

2008-07-30T16:10:10Z

References: Added external links to scanned images

← Older revision		Revision as of 18:10, 30 July 2008
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	*[[Monte Carlo in the microcanonical ensemble]]		*[[Monte Carlo in the microcanonical ensemble]]
	==References==		==References==
	# Josiah Willard Gibbs "On the Equilibrium of Heterogeneous Substances", Transactions of the Connecticut Academy '''III''' pp. 108-248 (1876)		# Josiah Willard Gibbs "On the Equilibrium of Heterogeneous Substances", Transactions of the Connecticut Academy '''III''' pp. 108-248 (1876) [http://gallica.bnf.fr/ark:/12148/bpt6k95192s (page images on gallica)]
	# Josiah Willard Gibbs "On the Equilibrium of Heterogeneous Substances", Transactions of the Connecticut Academy '''III''' pp. 343-524 (1878)		# Josiah Willard Gibbs "On the Equilibrium of Heterogeneous Substances", Transactions of the Connecticut Academy '''III''' pp. 343-524 (1878) [http://gallica.bnf.fr/ark:/12148/bpt6k95192s (page images on gallica)]
	# Josiah Willard Gibbs "Elementary principles in statistical mechanics developed with especial reference to the rational foundation of thermodynamics" (1902) [http://www.archive.org/download/elementaryprinci00gibbrich/elementaryprinci00gibbrich.pdf (scanned page images in PDF format)]		# Josiah Willard Gibbs "Elementary principles in statistical mechanics developed with especial reference to the rational foundation of thermodynamics" (1902) [http://www.archive.org/download/elementaryprinci00gibbrich/elementaryprinci00gibbrich.pdf (scanned page images in PDF format)]
	#[http://dx.doi.org/10.1002/andp.19023141007 A. Einstein "Kinetische Theorie des Wärmegleichgewichtes und des zweiten Hauptsatzes der Thermodynamik", Annalen der Physik '''9''' pp. 417-433 (1902)]		#[http://dx.doi.org/10.1002/andp.19023141007 A. Einstein "Kinetische Theorie des Wärmegleichgewichtes und des zweiten Hauptsatzes der Thermodynamik", Annalen der Physik '''9''' pp. 417-433 (1902)]

Carl McBride: Added classic references

2008-07-30T15:49:58Z

Added classic references

← Older revision		Revision as of 17:49, 30 July 2008
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	'''Thermostatistical ensembles''' are collectives whose average behaviour reflects the actual behaviour of a physical system. Ensembles are fundamental in the study of [[statistical mechanics]]. From one point of view they can be seen as mathematical labour-saving devices, given the intractability of following the trajectory of a macroscopic system in its journey through [[phase space]]. For example, celestial mechanics is hard enough, however, the [[Avogadro constant]] is on a par with the total number of stars in the universe. Clearly one needs a device that adequately represents the system of interest. Ensembles provide a link between the expectation value of physical observables (such as [[temperature]], [[internal energy]] etc.) and the individual motions of the plethora of constituent atoms and/or molecules.		'''Thermostatistical ensembles''' are collectives whose average behaviour reflects the actual behaviour of a physical system. Ensembles are fundamental in the study of [[statistical mechanics]]. From one point of view they can be seen as mathematical labour-saving devices, given the intractability of following the trajectory of a macroscopic system in its journey through [[phase space]]. For example, celestial mechanics is hard enough, however, the [[Avogadro constant]] is on a par with the total number of stars in the universe. Clearly one needs a device that adequately represents the system of interest. Ensembles provide a link between the expectation value of physical observables (such as [[temperature]], [[internal energy]] etc.) and the individual motions of the plethora of constituent atoms and/or molecules.
	==History==		==History==
	The concept of thermostatistical ensembles was introduced by [[Josiah Willard Gibbs]] (Ref. 1). [[Albert Einstein]] also ~~also, independently, introduced ensembles~~ (Refs. 2 and 3).		The concept of thermostatistical ensembles was introduced by [[Josiah Willard Gibbs]] (Ref. 1-3). [[Albert Einstein]] also made contributions (Refs. 4 and 5).
	==Representative ensembles==		==Representative ensembles==
	*[[Canonical ensemble]] (<math>NVT</math>)		*[[Canonical ensemble]] (<math>NVT</math>)
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	*[[Monte Carlo in the microcanonical ensemble]]		*[[Monte Carlo in the microcanonical ensemble]]
	==References==		==References==
			# Josiah Willard Gibbs "On the Equilibrium of Heterogeneous Substances", Transactions of the Connecticut Academy '''III''' pp. 108-248 (1876)
			# Josiah Willard Gibbs "On the Equilibrium of Heterogeneous Substances", Transactions of the Connecticut Academy '''III''' pp. 343-524 (1878)
	# Josiah Willard Gibbs "Elementary principles in statistical mechanics developed with especial reference to the rational foundation of thermodynamics" (1902) [http://www.archive.org/download/elementaryprinci00gibbrich/elementaryprinci00gibbrich.pdf (scanned page images in PDF format)]		# Josiah Willard Gibbs "Elementary principles in statistical mechanics developed with especial reference to the rational foundation of thermodynamics" (1902) [http://www.archive.org/download/elementaryprinci00gibbrich/elementaryprinci00gibbrich.pdf (scanned page images in PDF format)]
	#[http://dx.doi.org/10.1002/andp.19023141007 A. Einstein "Kinetische Theorie des Wärmegleichgewichtes und des zweiten Hauptsatzes der Thermodynamik", Annalen der Physik '''9''' pp. 417-433 (1902)]		#[http://dx.doi.org/10.1002/andp.19023141007 A. Einstein "Kinetische Theorie des Wärmegleichgewichtes und des zweiten Hauptsatzes der Thermodynamik", Annalen der Physik '''9''' pp. 417-433 (1902)]

Carl McBride: Added a little more to the introduction

2008-07-30T13:46:34Z

Added a little more to the introduction

← Older revision		Revision as of 15:46, 30 July 2008
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	'''Thermostatistical ensembles''' are collectives whose average behaviour reflects the actual behaviour of a physical system.		'''Thermostatistical ensembles''' are collectives whose average behaviour reflects the actual behaviour of a physical system. Ensembles are fundamental in the study of [[statistical mechanics]]. From one point of view they can be seen as mathematical labour-saving devices, given the intractability of following the trajectory of a macroscopic system in its journey through [[phase space]]. For example, celestial mechanics is hard enough, however, the [[Avogadro constant]] is on a par with the total number of stars in the universe. Clearly one needs a device that adequately represents the system of interest. Ensembles provide a link between the expectation value of physical observables (such as [[temperature]], [[internal energy]] etc.) and the individual motions of the plethora of constituent atoms and/or molecules.
	==History==		==History==
	The concept of thermostatistical ensembles was introduced by [[Josiah Willard Gibbs]] (Ref. 1). [[Albert Einstein]] also also, independently, introduced ensembles (Refs. 2 and 3).		The concept of thermostatistical ensembles was introduced by [[Josiah Willard Gibbs]] (Ref. 1). [[Albert Einstein]] also also, independently, introduced ensembles (Refs. 2 and 3).

Carl McBride: /* References */ Added a reference

2008-07-30T13:01:40Z

References: Added a reference

← Older revision		Revision as of 15:01, 30 July 2008
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	#[http://dx.doi.org/10.1002/andp.19023141007 A. Einstein "Kinetische Theorie des Wärmegleichgewichtes und des zweiten Hauptsatzes der Thermodynamik", Annalen der Physik '''9''' pp. 417-433 (1902)]		#[http://dx.doi.org/10.1002/andp.19023141007 A. Einstein "Kinetische Theorie des Wärmegleichgewichtes und des zweiten Hauptsatzes der Thermodynamik", Annalen der Physik '''9''' pp. 417-433 (1902)]
	#[http://dx.doi.org/10.1002/andp.19033160510 A. Einstein "Eine Theorie der Grundlagen der Thermodynamik", Annalen der Physik '''11''' pp. 170-187 (1903)]		#[http://dx.doi.org/10.1002/andp.19033160510 A. Einstein "Eine Theorie der Grundlagen der Thermodynamik", Annalen der Physik '''11''' pp. 170-187 (1903)]
			#[http://dx.doi.org/10.1103/PhysRev.57.1160 Richard C. Tolman "On the Establishment of Grand Canonical Distributions", Physical Review '''57''' pp. 1160-1168 (1940)]
	[[category: statistical mechanics]]		[[category: statistical mechanics]]

Carl McBride: Added some references.

2008-07-30T12:51:24Z

Added some references.

← Older revision		Revision as of 14:51, 30 July 2008
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	'''Thermostatistical ensembles''' are collectives whose average behaviour reflects the actual behaviour of a physical system.		'''Thermostatistical ensembles''' are collectives whose average behaviour reflects the actual behaviour of a physical system.
	==History==		==History==
	The concept of thermostatistical ensembles was introduced by [[Josiah Willard Gibbs]] (Ref. ?). [[Albert Einstein]] also also, independently, introduced ensembles (Refs. 2 and 3).		The concept of thermostatistical ensembles was introduced by [[Josiah Willard Gibbs]] (Ref. 1). [[Albert Einstein]] also also, independently, introduced ensembles (Refs. 2 and 3).
	==~~Frequently encountered~~ ensembles==		==Representative ensembles==
	*[[Canonical ensemble]] (<math>NVT</math>)		*[[Canonical ensemble]] (<math>NVT</math>)
	*[[Gibbs ensemble]]		*[[Gibbs ensemble]]
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	*[[Isothermal-isobaric ensemble]] (<math>NpT</math>)		*[[Isothermal-isobaric ensemble]] (<math>NpT</math>)
	*[[Microcanonical ensemble]] (<math>NVE</math>)		*[[Microcanonical ensemble]] (<math>NVE</math>)

	==See also==		==See also==
	*[[Gibbs ensemble Monte Carlo]]		*[[Gibbs ensemble Monte Carlo]]
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	*[[Monte Carlo in the microcanonical ensemble]]		*[[Monte Carlo in the microcanonical ensemble]]
	==References==		==References==
			# Josiah Willard Gibbs "Elementary principles in statistical mechanics developed with especial reference to the rational foundation of thermodynamics" (1902) [http://www.archive.org/download/elementaryprinci00gibbrich/elementaryprinci00gibbrich.pdf (scanned page images in PDF format)]
			#[http://dx.doi.org/10.1002/andp.19023141007 A. Einstein "Kinetische Theorie des Wärmegleichgewichtes und des zweiten Hauptsatzes der Thermodynamik", Annalen der Physik '''9''' pp. 417-433 (1902)]
			#[http://dx.doi.org/10.1002/andp.19033160510 A. Einstein "Eine Theorie der Grundlagen der Thermodynamik", Annalen der Physik '''11''' pp. 170-187 (1903)]
	[[category: statistical mechanics]]		[[category: statistical mechanics]]

Carl McBride: A first save

2008-07-30T12:25:58Z

A first save

New page

'''Thermostatistical ensembles''' are collectives whose average behaviour reflects the actual behaviour of a physical system.
==History==
The concept of thermostatistical ensembles was introduced by [[Josiah Willard Gibbs]] (Ref. ?). [[Albert Einstein]] also also, independently, introduced ensembles (Refs. 2 and 3).
==Frequently encountered ensembles==
*[[Canonical ensemble]] (<math>NVT</math>)
*[[Gibbs ensemble]]
*[[Grand canonical ensemble]] (<math>\mu VT</math>)
*[[Isothermal-isobaric ensemble]] (<math>NpT</math>)
*[[Microcanonical ensemble]] (<math>NVE</math>)

==See also==
*[[Gibbs ensemble Monte Carlo]]
*[[Monte Carlo in the grand-canonical ensemble]]
*[[Monte Carlo in the microcanonical ensemble]]
==References==
[[category: statistical mechanics]]

← Older revision		Revision as of 15:45, 12 January 2011
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	*[[Monte Carlo in the grand-canonical ensemble]]		*[[Monte Carlo in the grand-canonical ensemble]]
	*[[Monte Carlo in the microcanonical ensemble]]		*[[Monte Carlo in the microcanonical ensemble]]
			*[[Multicanonical ensemble]]

	==References==		==References==
	# Josiah Willard Gibbs "On the Equilibrium of Heterogeneous Substances", Transactions of the Connecticut Academy '''III''' pp. 108-248 (1876) [http://gallica.bnf.fr/ark:/12148/bpt6k95192s (page images on gallica)]		# Josiah Willard Gibbs "On the Equilibrium of Heterogeneous Substances", Transactions of the Connecticut Academy '''III''' pp. 108-248 (1876) [http://gallica.bnf.fr/ark:/12148/bpt6k95192s (page images on gallica)]