Editing Ensemble (mathematical physics) (section)

{{Short description|Idealization of a large number of atomic-sized systems}}
{{other uses|Ensemble (disambiguation)}}
{{Statistical mechanics|cTopic=Ensembles}}

In [[physics]], specifically [[statistical mechanics]], 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 set of systems of particles used in statistical mechanics to describe a single
system.<ref name="ensamble dictionary">{{cite encyclopedia |last=Rennie| first=Richard | author2=Jonathan Law| title=Oxford Dictionary of Physics |year=2019 | isbn=978-0198821472 | pages=458 ff| publisher=Oxford University Press }}</ref> The concept of an ensemble was introduced by [[Willard Gibbs|J. Willard Gibbs]] in 1902.<ref name="gibbs">{{cite book |last=Gibbs |first=Josiah Willard |author-link=Josiah Willard Gibbs |title=[[Elementary Principles in Statistical Mechanics]] |year=1902 |publisher=[[Charles Scribner's Sons]] |location=New York}}</ref>

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 system]]s from the laws of classical or quantum mechanics.<ref name="Kittel">{{cite book |last=Kittel |first=Charles |author-link=Charles Kittel |author2=Herbert Kroemer  |title=Thermal Physics, Second Edition |publisher=W.H. Freeman and Company |year=1980 |isbn=0-7167-1088-9 |location=San Francisco |pages=31 ff}}</ref><ref name="Landau">{{cite book |title=Statistical Physics |last=Landau |first=L.D.  |author2=Lifshitz, E.M.  |isbn=0-08-023038-5 |author-link=Lev Landau |year=1980 |publisher=Pergamon Press |pages=9 ff }}</ref>