Classical canonical free energy

Set

context $ Z(\beta) $ … canonical partition function (classical or quantum)
definiendum $F(\beta):=-\frac{1}{\beta} \mathrm{ln}(Z(\beta)) $

Discussion

This mirrors the Classical microcanonical entropy.

The usage of the free energy is similar to that of the cumulant-generating function.

Reference

Wikipedia: Cumulant-generating function

Context

Classical canonical partition function, Quantum canonical partition function