A statistical ensemble describes hypothetical copies of the same system under specified constraints, with a probability distribution over their microstates. An ensemble average is an expected value across those copies. The canonical ensemble fixes temperature and particle number while allowing energy exchange; the microcanonical ensemble fixes energy, and the grand canonical ensemble also allows particle exchange. These choices specify different physical preparations. [ref]
https://en.wikisource.org/wiki/Elementary_Principles_in_Statistical_Mechanics. Gibbs (1902), preface: ensembles of systems with different microscopic conditions
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