# 20.8: Entropy Can Be Expressed in Terms of a Partition Function

- Page ID
- 13722

We have seen that the partition function of a system gives us the key to calculate thermodynamic functions like energy or pressure as a moment of the energy distribution. We can extend this formulism to calculate the entropy of a system once its Q is known. The derivation is shown on page 840 and involves the use of the Stirling approximation. The end result is

\[S= \dfrac{U}{T} + k\ln Q \label{20.42}\]