Thermal equilibrium corresponds to the minimum free energy or maximum entropy at finite temperature. All equilibrium thermodynamic properties can be calculated by taking appropriate derivatives of the free energy with respect to its parameters.

Note: For non-interacting system of N particles, the partition function Z can be written as where is the partition function for a single particle. Consequently one obtains ideal gas behaviour for .

Thermodynamic quantities can be calculated by taking different derivatives of the free energy F as given below: