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classical_canonical_free_energy [2013/10/13 03:19] nikolaj |
classical_canonical_free_energy [2013/11/07 19:15] nikolaj |
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===== Classical canonical free energy === | ===== Classical canonical free energy === | ||
==== Definition ==== | ==== Definition ==== | ||
- | | @#88DDEE: $ Z(\beta) $ ... //classical// or //quantum// canonical partition function | | + | | @#88DDEE: $ Z(\beta) $ ... canonical partition function (classical or quantum) | |
| @#FFBB00: $F(\beta):=-\frac{1}{\beta} \mathrm{ln}(Z(\beta)) $ | | | @#FFBB00: $F(\beta):=-\frac{1}{\beta} \mathrm{ln}(Z(\beta)) $ | | ||
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==== Discussion ==== | ==== Discussion ==== | ||
This mirrors the [[Classical microcanonical entropy]]. | This mirrors the [[Classical microcanonical entropy]]. | ||
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+ | The usage of the free energy is similar to that of the cumulant-generating function. | ||
+ | === Reference === | ||
+ | Wikipedia: [[http://en.wikipedia.org/wiki/Cumulant-generating_function|Cumulant-generating function]] | ||
==== Parents ==== | ==== Parents ==== | ||
=== Requirements === | === Requirements === | ||
[[Classical canonical partition function]], [[Quantum canonical partition function]] | [[Classical canonical partition function]], [[Quantum canonical partition function]] |