The Statistical ensemble reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Statistical ensemble

In physics, a statistical ensemble is a very large set of similar systems, considered all at once.

The topic of statistical ensembles is important in thermodynamics, statistical mechanics and quantum physics.

In quantum physics, there are two types of ensembles:

• Pure ensembles cannot be decomposed into different subensembles. A ray in a Hilbert space can represent such an ensemble in quantum mechanics, although a density matrix may also be used. Thus a pure ensemble corresponds to having many copies of the same (up to a global phase) quantum state.
• Mixed ensembles are decomposable into different (pure) subensembles. A density matrix represents such an ensemble in quantum mechanics; it cannot be represented as a ray in a Hilbert space. In general, an infinite number of distinct decompositions will be possible.

A decomposition of a mixed ensemble corresponds to expressing the density matrix describing the ensemble as a convex-linear sum of other density matrices, e.g. projection operators.

See also

• density matrix
• Partition function (statistical mechanics)
• microcanonical ensemble
• canonical ensemble
• grand canonical ensemble
• isothermal-isobaric ensemble

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