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classical_canonical_ensemble [2013/11/05 19:03] nikolaj |
classical_canonical_ensemble [2015/08/18 20:30] nikolaj |
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| ===== Classical canonical ensemble === | ===== Classical canonical ensemble === | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#FFBB00: $ \langle \mathcal M, H,{\hat\rho}\rangle \in \mathrm{it} $ | | + | | @#FFBB00: definiendum | @#FFBB00: $ \langle \mathcal M, H,{\hat\rho}\rangle \in \mathrm{it} $ | |
| + | | @#55EE55: postulate | @#55EE55: $\langle \mathcal M, H,{\hat\rho},{\hat\rho}_0\rangle$ ... classical statistical ensemble | | ||
| + | | @#55EE55: postulate | @#55EE55: $\hat\rho: \mathbb R\to(\Gamma_{\mathcal M} \to\mathbb R_+) $ | | ||
| + | | @#55EE55: postulate | @#55EE55: $\hat\rho(\beta;{\bf q},{\bf p}):=\mathrm{e}^{-\beta\ H({\bf q},{\bf p})}$ | | ||
| - | | @#55EE55: $\langle \mathcal M, H,{\hat\rho},{\hat\rho}_0\rangle$ ... classical statistical ensemble | | + | ----- |
| - | + | === Discussion === | |
| - | + | ||
| - | | @#55EE55: $\hat\rho: \mathbb R\to(\Gamma_{\mathcal M} \to\mathbb R_+) $ | | + | |
| - | | @#55EE55: $\hat\rho(\beta;{\bf q},{\bf p}):=\mathrm{e}^{-\beta\ H({\bf q},{\bf p})}$ | | + | |
| - | + | ||
| - | ==== Discussion ==== | + | |
| == Equivalence of the microcanonical and canonical ensemble == | == Equivalence of the microcanonical and canonical ensemble == | ||
| Line 24: | Line 22: | ||
| Wikipedia: | Wikipedia: | ||
| [[http://en.wikipedia.org/wiki/Microcanonical_ensemble|Canonical ensemble]], [[http://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_statistics|Maxwell–Boltzmann statistics]] | [[http://en.wikipedia.org/wiki/Microcanonical_ensemble|Canonical ensemble]], [[http://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_statistics|Maxwell–Boltzmann statistics]] | ||
| - | ==== Parents ==== | + | |
| + | ----- | ||
| === Refinement of === | === Refinement of === | ||
| [[Classical statistical ensemble]] | [[Classical statistical ensemble]] | ||
| - | === Requirements === | + | === Context === |
| [[Exponential function]] | [[Exponential function]] | ||
