Canonical ensemble convention

The canonical ensemble describes a system in thermal equilibrium with a heat bath at fixed temperature $T$. The system can exchange energy with the bath but has fixed volume $V$ and particle number $N$.

Probability distribution

In the canonical ensemble, the probability of finding the system in microstate $(q, p)$ is

where:

• $\beta = 1/(k_B T)$ is the inverse temperature
• $H$ is the Hamiltonian
• $Z$ is the canonical partition function

The natural thermodynamic potential for this ensemble is the Helmholtz free energy . The bath is modeled as a thermal reservoir . For the full formal definition, see canonical ensemble .