 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-344/1/a/solution

Codex  0 Created 2026-09-29 Updated 2026-10-03

\int ϕ d r = Φ

μ_{0}

. Stationarity of

F [ϕ] - μ_{0} \int ϕ d r

under every local variation gives

\frac{δ F}{δ ϕ ( r )} = μ (r) = μ_{0} .

Thus the chemical potential is spatially constant at constrained equilibrium.

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