Canonical ensemble

Summary

The canonical ensemble describes a system with a fixed number of particles in contact with a heat bath at a fixed temperature $T$. It gives each microstate of energy $E$ a weight proportional to $e^{-E / (k_B T)}$, the Boltzmann distribution. The normalizing constant $Z$ is the partition function, and the free energy $F = -k_B T \ln Z$ gives all thermodynamic quantities by differentiation. It is the ensemble used most often in calculations, because independent parts of a system give independent factors of $Z$.