# Canonical Ensemble

Also found in: Wikipedia.

## 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 ?
The canonical ensemble is used, in which a temperature coefficient is introduced to keep the temperature constant.
However, both the shape and size of computational domain are unchangeable in canonical ensemble, the space of liquid must be expansive as the increase of distance between atoms.
In the canonical ensemble with fixed electric charge, there is a first-order phase transition between small and large black holes [9-12].
Based on the extended first law, the black hole's phase transition property will be investigated in canonical ensemble with fixed electric charge and topological charge.
To study problems of the canonical ensemble, we focus on the calculation the canonical density matrix and the Helmholtz free energy of a single particle under asymmetric harmonic oscillator potential.
We may suppose that, because of thermal interaction between the absorber and particles just outside the absorber, the absorber ensemble at [T.sub.1] will evolve into an ensemble at t - r/c - dt which is close to the canonical ensemble, and which, like the canonical ensemble, lies almost entirely outside C (i.e., the probability distribution which is the ensemble assigns C a probability near 0).
Wang, "Critical behavior of charged Gauss-Bonnet-AdS black holes in the grand canonical ensemble, " Physical Review D-Particles, Fields, Gravitation and Cosmology, vol.
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. The final 60 pages present problems in various areas such as fluids, waves, and thermodynamics.
In [59], the authors concentrated their efforts on the Ehrenfest equation in the grand canonical ensemble. So it is worthwhile to study the phase transition in canonical ensemble.

Site: Follow: Share:
Open / Close