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In mathematical physics, especially as introduced into statistical mechanics and thermodynamics by J. Willard Gibbs in 1902, an ensemble (also statistical ensemble) is an idealization consisting of a large number of virtual copies (sometimes infinitely many) of a system, considered all at once, each of which represents a possible state that the real system might be in. In other words, a statistical ensemble is a probability distribution for the state of the system. A thermodynamic ensemble is a specific variety of statistical ensemble that, among other properties, is in statistical equilibrium (defined below), and is used to derive the properties of thermodynamic systems from the laws of classical or quantum mechanics. This article treats the notion of ensembles in a mathematically rigorous fashion, although relevant physical aspects will be mentioned. == 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 indeed, to include every possible microscopic state the system could be in, consistent with its observed macroscopic properties. But for important physical cases it can be 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 (see below). Some of these results are presented in the statistical mechanics article. The concept of an equilibrium or stationary ensemble is crucial to some 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 equally contains all past and future phases of the system. Such a statistical ensemble, that does not change over time, is called ''stationary'' or said to be in ''statistical equilibrium''.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Statistical ensemble (mathematical physics)」の詳細全文を読む スポンサード リンク
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