Grand potential

Set

 context $\Xi(\beta,\mu)$ … grand canonical partition function definiendum $\Omega(\beta,\mu):=-\frac{1}{\beta}\,\mathrm{ln}(\Xi(\beta,\mu))$

Discussion

This mirrors the classical microcanonical entropy and the classical canonical free energy. Also, think $\rho \sim {\mathrm e}^{-H/T}$ or $H \sim -T \ln(\rho)$.

Reference

Wikipedia Grand potential