Characteristic state function

The characteristic state function or Massieu's potential[1] 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

edit
  • 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

edit
  1. ^ Balian, Roger (2017-11-01). "François Massieu and the thermodynamic potentials". Comptes Rendus Physique. 18 (9–10): 526–530. Bibcode:2017CRPhy..18..526B. doi:10.1016/j.crhy.2017.09.011. ISSN 1631-0705. "Massieu's potentials [...] are directly recovered as logarithms of partition functions."