Characteristic state function

The characteristic state function in statistical mechanics refers to a particular relationship between the partition function of an ensemble.

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In particular, if the partition function P satisfies

P = exp( − βQ) or P = exp( + βQ)

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.

Examples

• 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.