User:EditingPencil/sandbox/ensembles

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!Microcanonical

!Canonical

!Gibbs Canonical

!Grand Canonical

!Isoenthalpic–isobaric ensemble{{Cite journal |last=Haile |first=J.M. |last2=Graben |first2=H.W. |date=1980-08-20 |title=On the isoenthalpic-isobaric ensemble in classical statistical mechanics |url=http://www.tandfonline.com/doi/abs/10.1080/00268978000102391 |journal=Molecular Physics |language=en |volume=40 |issue=6 |pages=1433–1439 |doi=10.1080/00268978000102391 |issn=0026-8976}}

|$P(\backslash mu\_i)=e^\{-ST\backslash beta\}=\backslash frac\; 1\; \backslash Omega$

|$P(\backslash mu\_i)=e^\{-ST\backslash beta\}=\backslash frac\{e^\{-E\backslash beta\}\}\; Z$

|$P(\backslash mu\_i)=e^\{-ST\backslash beta\}=\backslash frac\{e^\{-H\backslash beta\}\}\; Z$

|$P(\backslash mu\_i)=e^\{-ST\backslash beta\}=\backslash frac\{e^\{-(E-\backslash mu\; N)\backslash beta\}\}\; Z$

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|$\backslash Omega\; =\backslash sum\_i\; 1$

|$Z=\backslash sum\_i\; e^\{-\backslash frac\{E(\backslash mu\_i)\}\{K\_BT\}\}$

|$Z=\backslash sum\_i\; e^\{-\backslash frac\{H(\backslash mu\_i)\}\{K\_BT\}\}$

|$Z=\backslash sum\_i\; e^\{-\backslash frac\{E(\backslash mu\_i)-\backslash mu\; N(\backslash mu\_i)\}\{K\_BT\}\}=\backslash sum\_i\; e^\{-\backslash frac\; \{L(\backslash mu\_i)\}\; \{K\_BT\}\}$

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|$S\; =\; K\_B\; \backslash log(\backslash Omega)$

|$S\; =\; K\_B\; \backslash log(\backslash mathcal\; Z)\; +\; K\_B\; \backslash beta\; E$

|$S\; =\; K\_B\; \backslash log(\backslash mathcal\; Z)\; +\; K\_B\; \backslash beta\; H$

|$S\; =\; K\_B\; \backslash log(\backslash mathcal\; Z)\; +\; K\_B\; \backslash beta\; (E\; -\; \backslash mu\; N)$

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|$\backslash Omega(N,\; V\; ,\; E\; )\; =\; e^\{\backslash frac\; S\; \{\; K\_B\}\}$

|$\backslash mathcal\; Z(N,V,T)=e^\{-\backslash frac\; F\; \{K\_B\; T\}\}$

|$\backslash mathcal\; Z(N,P,T\; )=e^\{-\backslash frac\; G\{K\_BT\}\}$

|$\backslash mathcal\; Z(\backslash mu,V,T)=e^\{-\backslash frac\; \backslash Phi\; \{K\_BT\}\}$

|$\backslash mathcal\; Z(N,P,H)$

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|$-\backslash frac\{\backslash partial\}\{\backslash partial\; \backslash beta\}(\backslash log\; \backslash mathcal\; Z)\; =\; \backslash langle\; E\; \backslash rangle$

|$-\backslash frac\{\backslash partial\}\{\backslash partial\; \backslash beta\}(\backslash log\; \backslash mathcal\; Z)\; =\; \backslash langle\; H\; \backslash rangle$

|$-\backslash frac\{\backslash partial\}\{\backslash partial\; \backslash beta\}(\backslash log\; \backslash mathcal\; Z)\; =\; \backslash langle\; E\; \backslash rangle\; -\; \backslash mu\; \backslash langle\; N\; \backslash rangle$

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|$P\; =\backslash frac\; 1\; \backslash beta\; \backslash frac\{\backslash partial\backslash log(\backslash Omega)\}\{\backslash partial\; V\}$

|$P\; =\backslash frac\; 1\; \backslash beta\; \backslash frac\{\backslash partial\backslash log(\backslash mathcal\; Z)\}\{\backslash partial\; V\}$

|$V\; =-\; \backslash frac\; 1\; \backslash beta\; \backslash frac\{\backslash partial\backslash log(\backslash mathcal\; Z)\}\{\backslash partial\; P\}$

|$N\; =\; \backslash frac\; 1\; \backslash beta\; \backslash frac\{\backslash partial\backslash log(\backslash mathcal\; Z)\}\{\backslash partial\; \backslash mu\}$

|$V\; =-\; \backslash frac\; 1\; \backslash beta\; \backslash frac\{\backslash partial\backslash log(\backslash mathcal\; Z)\}\{\backslash partial\; P\}$

|$\backslash mu\; =-\backslash frac\; 1\; \backslash beta\; \backslash frac\{\backslash partial\backslash log(\backslash mathcal\; Z)\}\{\backslash partial\; N\}$

|$\backslash mu\; =-\backslash frac\; 1\; \backslash beta\; \backslash frac\{\backslash partial\backslash log(\backslash mathcal\; Z)\}\{\backslash partial\; N\}$

|$P\; =\; -\backslash frac\; 1\; \backslash beta\; \backslash frac\{\backslash partial\backslash log(\backslash mathcal\; Z)\}\{\backslash partial\; V\}$

|$\backslash mu\; =-\backslash frac\; 1\; \backslash beta\; \backslash frac\{\backslash partial\backslash log(\backslash mathcal\; Z)\}\{\backslash partial\; N\}$

|$S\; =\; -\; \backslash frac\{\backslash partial\; F\}\{\backslash partial\; T\}$

|$S\; =\; -\; \backslash frac\{\backslash partial\; G\}\{\backslash partial\; T\}$

|$S\; =\; -\; \backslash frac\{\backslash partial\; \backslash Phi\; \}\{\backslash partial\; T\}$

|$\backslash beta\; =\; \backslash frac\{\backslash partial\backslash log(\backslash mathcal\; Z)\}\{\backslash partial\; H\}$

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!Grand isobaric adiabatic ensemble

!Grand isochoric adiabatic ensemble

!Guggenheim ensemble

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|$P(\backslash mu\_i)=e^\{-ST\backslash beta\}=\backslash frac\{e^\{-(E+PV-\backslash mu\; N)\backslash beta\}\}\; Z$

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|$Z=\backslash sum\_i\; e^\{-\backslash frac\{E(\backslash mu\_i)+PV(\backslash mu\_i)-\backslash mu\; N(\backslash mu\_i)\}\{K\_BT\}\}=\backslash sum\_i\; e^\{-\backslash frac\; \{R(\backslash mu\_i)\}\; \{K\_BT\}\}$

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