Grand potential

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 $H \sim -T \ln(\rho)$ .