Grand Partition Function

#Physics

$\displaystyle \mathbb{Z}=\sum_{\text{ASN}}e^{\beta(\mu N-\varepsilon)}$

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

$\displaystyle \mathbb{Z}=\sum_{\text{ASN}}\lambda ^Ne^{-\beta \varepsilon}$

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