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grand_potential [2015/08/16 13:28] nikolaj |
grand_potential [2015/08/16 14:27] nikolaj |
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| ==== Set ==== | ==== Set ==== | ||
| | @#55CCEE: context | @#55CCEE: $ \Xi(\beta,\mu) $ ... grand canonical partition function | | | @#55CCEE: context | @#55CCEE: $ \Xi(\beta,\mu) $ ... grand canonical partition function | | ||
| - | | @#FFBB00: definiendum | @#FFBB00: $ \Omega(\beta,\mu):=-\frac{1}{\beta} \mathrm{ln}(\Xi(\beta,\mu)) $ | | + | | @#FFBB00: definiendum | @#FFBB00: $ \Omega(\beta,\mu):=-\frac{1}{\beta}\,\mathrm{ln}(\Xi(\beta,\mu)) $ | |
| ----- | ----- | ||
| === Discussion === | === Discussion === | ||
| - | This mirrors the [[classical microcanonical entropy]] and the [[classical canonical free energy]]. | + | This mirrors the [[classical microcanonical entropy]] and the [[classical canonical free energy]]. Also, think $\rho \sim {\mathrm e}^{-H/T}$ or $H \sim -T \ln(\rho)$. |
| === Reference === | === Reference === | ||
| Wikipedia [[http://en.wikipedia.org/wiki/Grand_potential|Grand potential]] | Wikipedia [[http://en.wikipedia.org/wiki/Grand_potential|Grand potential]] | ||
