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( − βQ) or P = exp( + βQ)
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.
[edit] Examples
- The microcanonical ensemble satisfies hence, its characteristic state function is This quantity roughly speaking, denotes the energy of the entropy at a particular temperature.
- 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 total Pressure-volume work.
- The isothermal-isobaric ensemble satisfies so its characteristic function is the Gibbs free energy.