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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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.


The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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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.
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