The characteristic state function or Massieu's potential 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 References Statistical mechanics