Statistical Mechanics - Statistical Ensembles

Statistical Ensembles

See also: Statistical ensemble

The modern formulation of statistical mechanics is based on the description of the physical system by an ensemble that represents all possible configurations of the system and the probability of realizing each configuration.

Each ensemble is associated with a partition function that, with mathematical manipulation, can be used to extract values of thermodynamic properties of the system. According to the relationship of the system to the rest of the universe, one of three general types of ensembles may apply, in order of increasing complexity:

  • Microcanonical ensemble: describes a completely isolated system, having constant energy, as it does not exchange energy or mass with the rest of the universe.
  • Canonical ensemble: describes a system in thermal equilibrium with its environment. It may only exchange energy in the form of heat with the outside.
  • Grand-canonical ensemble: used in open systems which exchange energy and mass with the outside.
Summary of ensembles Ensembles
Microcanonical Canonical Grand canonical
Variables (suppressed

constant for ensemble)

E, N, V T, N, V T, μ, V
Microscopic features
  • Number of microstates
  • Canonical partition function
  • Grand canonical partition function
Macroscopic function

Read more about this topic:  Statistical Mechanics