| context | $ \Xi(\beta,\mu) $ … grand canonical partition function |
| definiendum | $ \Omega(\beta,\mu):=-\frac{1}{\beta}\,\mathrm{ln}(\Xi(\beta,\mu)) $ |
This mirrors the classical microcanonical entropy and the classical canonical free energy. Also, think $\rho \sim {\mathrm e}^{-H/T}$ or $H \sim -T \ln(\rho)$.
Wikipedia Grand potential