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caloric_equation_of_state [2013/10/13 16:01] nikolaj |
caloric_equation_of_state [2014/03/21 11:11] (current) |
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| ===== Caloric equation of state ===== | ===== Caloric equation of state ===== | ||
| ==== Theorem ==== | ==== Theorem ==== | ||
| - | | @#88DDEE: $ \Omega(\beta,\mu) $ ... grand potential | | + | | @#55CCEE: context | @#55CCEE: $ \Omega(\beta,\mu) $ ... grand potential | |
| - | | @#55EE55: $ U = \frac{\partial}{\partial\beta}(\beta\ \Omega) + \mu\ \langle\hat N\rangle $ | | + | | @#55EE55: postulate | @#55EE55: $ U = \frac{\partial}{\partial\beta}(\beta\ \Omega) + \mu\ \langle\hat N\rangle $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| - | One can use the [[thermal equation of state]] to express $\langle\hat N\rangle$ in terms of $\Omega(\beta,\mu)$. | ||
| ==== Parents ==== | ==== Parents ==== | ||
| - | === Requirements === | + | === Context === |
| - | [[Particle number expectation value]], [[grand potential]] | + | [[Particle number expectation value]], [[Grand potential]] |
