# 4.9: Summary of Major Ensembles

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 boundary variables probability of microstate p.f. master function microcanonical adiabatic (no-skid) E, V, N $$\frac{d \Gamma}{N ! h_{0}^{3 N}} \frac{1}{\Omega} \text { or } 0$$ Ω S(E, V, N) = kB ln Ω canonical heat bath T, V, N $$\frac{d \Gamma e^{-\beta H(\Gamma)}}{N ! h_{0}^{3 N}} \frac{1}{Z}$$ Z F(T, V, N) = −kBT lnZ grand canonical heat bath, with holes T, V, μ $$\frac{d \Gamma_{N} e^{-\beta H\left(\Gamma_{N}\right)-\alpha N}}{N ! h_{0}^{3 N}} \frac{1}{\Xi}$$ Ξ Π(T, V, µ) = −kBT ln Ξ

In all cases, the partition function (p.f. in the above table) is the normalization factor

$\mathrm{p.f.}=\sum_{\text { microstates }} \text { unnormalized probability. }$

4.9: Summary of Major Ensembles is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.