Samiksha Jaiswal (Editor)

Characteristic state function

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The characteristic state function 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 ⁡ ( − β Q ) or P = exp ⁡ ( + β Q )

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 Ω ( U , V , N ) = e β T S hence, its characteristic state function is T S .
  • The canonical ensemble satisfies Z ( T , V , N ) = e − β A hence, its characteristic state function is the Helmholtz free energy A .
  • The grand canonical ensemble satisfies Z ( T , V , μ ) = e − β Φ , so its characteristic state function is the Grand potential Φ .
  • The isothermal-isobaric ensemble satisfies Δ ( N , T , P ) = e − β G so its characteristic function is the Gibbs free energy G .

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

    References

    Characteristic state function Wikipedia
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