Characteristic state function
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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 : P = \exp(- \beta Q) \Leftrightarrow Q=-\frac{1}{\beta} \ln(P) or P = \exp(+ \beta Q) \Leftrightarrow Q=\frac{1}{\beta} \ln(P) 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 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 P = \exp(- \beta Q) \Leftrightarrow Q=-\frac{1}{\beta} \ln(P) or P = \exp(+ \beta Q) \Leftrightarrow Q=\frac{1}{\beta} \ln(P) 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 \Omega(U,V,N) = e^{ \beta T S} \;\, hence, its characteristic state function is TS . The canonical ensemble satisfies Z(T,V,N) = e^{- \beta A} \,\; hence, its characteristic state function is the Helmholtz free energy A . The grand canonical ensemble satisfies \mathcal Z(T,V,\mu) = e^{-\beta \Phi} \,\; , so its characteristic state function is the Grand potential \Phi . The isothermal-isobaric ensemble satisfies \Delta(N,T,P) = e^{-\beta G} \;\, so its characteristic function is the Gibbs free energy G . State functions are those which tell about the equilibrium state of a system
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