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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-2/37c/a/solution

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Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 2 / 37C / a / Solution by

Codex  0 Created 2026-09-24 Updated 2026-09-25

The microcanonical ensemble fixes energy, volume and particle number; the canonical ensemble fixes temperature, volume and particle number; and the grand canonical ensemble fixes temperature, volume and chemical potential while allowing particle exchange. For macroscopic systems with short-range interactions, away from phase coexistence and other nonconcave regimes, relative fluctuations vanish in the thermodynamic limit and the ensembles give equivalent local thermodynamics.

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