# Canonical Ensemble

(redirected from Canonical partition function)

## canonical ensemble

[kə′nän·ə·kəl än′säm·bəl]
(statistical mechanics)
A hypothetical collection of systems of particles used to describe an actual individual system which is in thermal contact with a heat reservoir but is not allowed to exchange particles with its environment.

## Canonical Ensemble

a statistical ensemble for macroscopic systems (such as a crystal or a gas in a vessel) that are in thermal contact with an environment whose temperature is constant. Such systems may be considered as small parts (subsystems) of a large closed system in a state of thermal equilibrium. In canonical ensembles the interaction of a subsystem with the remainder of the closed system (the “thermostat”) is characteristically assumed to be weak, so that the energy of the interaction is negligible in comparison with the energy of the subsystem. Therefore it is possible to speak of the energy of the subsystem as a definite quantity. However, interaction between the subsystem and the thermostat leads to exchange of energy between them, as a result of which the subsystem may exist in different energy states. The distribution of the probability of different microscopic states of the subsystem (that is, states defined by the values of the coordinates and velocities of all particles of the subsystem) is given by a canonical Gibbs distribution.

The concept of the canonical ensemble was introduced by J. W. Gibbs; it makes it possible easily to obtain the basic results of statistical physics and, in particular, to derive the laws of thermodynamics.

G. IA. MIAKISHEV

References in periodicals archive ?
where F = F(T, V, N) stands for the Helmholtz free energy given by F = -[k.sub.B]T ln [Z.sub.N,V]([beta]) = U - TS with [mathematical expression not reproducible] the canonical partition function. The sum is made over the energies [E.sub.N,V] of all possible configurations with exactly N fermions in the volume V.
Also the number of photons is not conserved and there is no condition on the number of photons, so the canonical partition function, according to Bose-Einstein statistics, is given by
Among his topics are the canonical partition function, chemical reactions in ideal gases, integral equation theories for the radial distribution functions, and perturbation theory.

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