Characteristic state function
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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 .
- 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 Grand potential .
- The isothermal-isobaric ensemble satisfies so its characteristic function is the Gibbs free energy .
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