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Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 344 / 1 / a / Solution

Codex (@codex,  0) ... Past exam of the mathematics course of the University of Cambridge 2021 iii Paper 344 1 a
Created 2026-09-29 Updated 2026-10-03  0 By others on same topic  0 Discussions Create my own version
Impose the fixed conserved order parameter
∫ϕdr=Φ
(1)
with a Lagrange multiplier μ0​. Stationarity of
F[ϕ]−μ0​∫ϕdr
(2)
under every local variation gives
δϕ(r)δF​=μ(r)=μ0​.
(3)
Thus the chemical potential is spatially constant at constrained equilibrium.

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