Editing Ensemble (mathematical physics) (section)

== Physical considerations ==

The ensemble formalises the notion that an experimenter repeating an experiment again and again under the same macroscopic conditions, but unable to control the microscopic details, may expect to observe a range of different outcomes.

The notional size of ensembles in thermodynamics, statistical mechanics and [[quantum statistical mechanics]] can be very large, including every possible [[microstate (statistical mechanics)|microscopic state]] the system could be in, consistent with its observed [[macroscopic]] properties. For many important physical cases, it is possible to calculate averages directly over the whole of the thermodynamic ensemble, to obtain explicit formulas for many of the thermodynamic quantities of interest, often in terms of the appropriate [[partition function (mathematics)|partition function]].

The concept of an equilibrium or stationary ensemble is crucial to many applications of statistical ensembles. Although a mechanical system certainly evolves over time, the ensemble does not necessarily have to evolve. In fact, the ensemble will not evolve if it contains all past and future phases of the system. Such a statistical ensemble, one that does not change over time, is called ''stationary'' and can be said to be in ''statistical equilibrium''.<ref name="gibbs"/>

=== Terminology ===

* The word "ensemble" is also used for a smaller set of possibilities [[sample (statistics)|sampled]] from the full set of possible states.  For example, a collection of [[random walk|walkers]] in a [[Markov chain Monte Carlo]] iteration is called an ensemble in some of the literature.
* The term "ensemble" is often used in physics and the physics-influenced literature.  In [[probability theory]], the term [[probability space]] is more prevalent.