The characteristic state function
in statistical mechanics
refers to a particular relationship between the partition function
of an ensemble.
In particular, if the partition function P satisfies
in which Q is a thermodynamic quantity, then Q is known as the "characteristic state function" of the ensemble corresponding to "P". Beta refers to the thermodynamic beta.
- The microcanonical ensemble satisfies hence, its characteristic state function is This quantity roughly speaking, denotes the energy of the entropy at a particular temperature.
- The canonical ensemble satisfies hence, its characteristic state function is the Helmholtz free energy.
- The grand canonical ensemble satisfies , so its characteristic state function is the total Pressure-volume work.
- The isothermal-isobaric ensemble satisfies so its characteristic function is the Gibbs free energy.