Fugacity (statistical mechanics, $z=e^{\beta \mu }$)

The dimensionless quantum gas fugacity weights particle number in the grand canonical ensemble: a state with energy $E$ and particle number $N$ has weight $z^N{e}^{-\beta E}$. The chemical potential and one-particle energies must use the same reference. When the lowest one-particle energy is zero, $z\ll 1$ makes both fermion and boson occupations small throughout the low-energy spectrum. This dimensionless quantity must be distinguished from the pressure-valued fugacity used in chemical thermodynamics.