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Classical microcanonical phase volume
Definition
| $ \langle \mathcal M, \mathcal H,\pi,\pi_0,{\hat\rho},{\hat\rho}_0\rangle$ … classical microcanonical ensemble |
| $ \mathrm{dim}(\mathcal M) = 3N $ |
| $ \hbar$ … Reduced Planck's constant |
| $\Gamma(E):=\frac{1}{h^{3N} N!}\int_{\{\langle{\bf q},{\bf p}\rangle\in \Gamma_{\mathcal M}\ |\ E\le H({\bf q},{\bf p})\le E+\Delta\}} \mathrm d\Gamma $ |
Discussion
Alternative definitions
$\Gamma(E):=\frac{1}{h^{3N}N!}\int_{\Gamma_{\mathcal M}} \hat\rho(E;{\bf q},{\bf p}) \ \mathrm d\Gamma $
And here we see that this is the analog of Classical canonical partition function for the Classical canonical ensemble.
Parents
Requirements
