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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. |
| ==History== | | ==History== |
| The concept of thermostatistical ensembles was introduced by [[Josiah Willard Gibbs]] (Ref. 1-3). [[Albert Einstein]] also made contributions (Refs. 4 and 5). | | The concept of thermostatistical ensembles was introduced by [[Josiah Willard Gibbs]] (Ref. ?). [[Albert Einstein]] also also, independently, introduced ensembles (Refs. 2 and 3). |
| ==Representative ensembles== | | ==Frequently encountered ensembles== |
| *[[Canonical ensemble]] (<math>NVT</math>) | | *[[Canonical ensemble]] (<math>NVT</math>) |
| *[[Gibbs ensemble]] | | *[[Gibbs ensemble]] |
| *[[Grand canonical ensemble]] (<math>\mu VT</math>) | | *[[Grand canonical ensemble]] (<math>\mu VT</math>) |
| *[[Isoenthalpic–isobaric ensemble]] (<math>NpH</math>)
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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>) |
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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]]
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| ==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)]
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| # 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)]
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| # 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)]
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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)]
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| #[http://dx.doi.org/10.1002/andp.19033160510 A. Einstein "Eine Theorie der Grundlagen der Thermodynamik", Annalen der Physik '''11''' pp. 170-187 (1903)]
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| #[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)]
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| [[category: statistical mechanics]] | | [[category: statistical mechanics]] |