# Canonical Ensemble

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## 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 ?
This model is known in statistical thermodynamics as the canonical ensemble.
In this case, we have [phi](I) = exp(F(I)/kT) for all I; then the process leads [rho] to the equilibrium distribution of the Gibbs canonical ensemble.
Here we invoke a temporal asymmetry: that thermal interaction carries ensembles into the canonical ensemble, but not out of it: a canonical ensemble now will evolve into a canonical ensemble later, but it can have come from an ensemble very unlike the canonical ensemble.
The author covers the microcanonical ensemble, the canonical ensemble, the grand canonical ensemble, and all their applications, as well as a wide variety of other related subjects and special topics in the field of thermodynamics and statistical mechanics.
His topics include elastic solids in series and parallel, Bernoulli's equation, through the Earth and back, impedance and power, the linear superposition of right-moving harmonic waves, through a glass darkly, convective and conductive heat flow, thermodynamic cycles and heat engines, and the canonical ensemble.

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