The potential of interest in this case is Helmholtz' free energy. It relates the expectation value of the energy at a given temperatur \( T \) to the entropy at the same temperature via $$ \begin{equation*} F=-k_{B}TlnZ=\langle E \rangle-TS. \end{equation*} $$
Helmholtz' free energy expresses the struggle between two important principles in physics, namely the strive towards an energy minimum and the drive towards higher entropy as the temperature increases. A higher entropy may be interpreted as a larger degree of disorder. When equilibrium is reached at a given temperature, we have a balance between these two principles. The numerical expression is Helmholtz' free energy.