Английская Википедия:Characteristic state function

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Шаблон:Short description Шаблон:Refimprove 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

<math>P = \exp(- \beta Q) \Leftrightarrow Q=-\frac{1}{\beta} \ln(P) </math> or <math>P = \exp(+ \beta Q) \Leftrightarrow Q=\frac{1}{\beta} \ln(P) </math>

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 <math> \Omega(U,V,N) = e^{ \beta T S} \;\, </math> hence, its characteristic state function is <math>TS</math>.
• The canonical ensemble satisfies <math>Z(T,V,N) = e^{- \beta A} \,\;</math> hence, its characteristic state function is the Helmholtz free energy <math>A</math>.
• The grand canonical ensemble satisfies <math>\mathcal Z(T,V,\mu) = e^{-\beta \Phi} \,\; </math>, so its characteristic state function is the Grand potential <math>\Phi</math>.
• The isothermal-isobaric ensemble satisfies <math>\Delta(N,T,P) = e^{-\beta G} \;\, </math> so its characteristic function is the Gibbs free energy <math>G</math>.

State functions are those which tell about the equilibrium state of a system

References

Шаблон:Thermodynamics-stub Шаблон:Statisticalmechanics-stub