Characteristic state function

From Wikipedia, the free encyclopedia
Jump to: navigation, search

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

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