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]
An isolated energy shell gives the microcanonical ensemble; a heat bath fixes for the canonical ensemble; a heat and particle reservoir fixes for the grand canonical ensemble. Constraints determine the allowed fluctuations and which thermodynamic potential is useful.

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