Grand Partition Function

$\mathbb{Z}=\sum _{\text{ASN}}{e}^{\beta (\mu N-\epsilon )}$

• $\mathbb{Z}$ it the partition function for the grand canonical ensemble
• $\text{ASN}$ denotes all states for all numbers of particles

$\mathbb{Z}=\sum _{\text{ASN}}{\lambda }^N{e}^{-\beta \epsilon }$

• $\lambda$ is the absolute activity
• $N$ is the number of particles at this energy level