The characteristic state function or Massieu's potential "Massieu's potentials [...] are directly recovered as logarithms of partition functions." in statistical mechanics refers to a particular relationship between the partition function of an ensemble.
In particular, if the partition function P satisfies
or
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 . 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 .
State functions are those which tell about the equilibrium state of a system
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