Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 353 / 2 / a / i / Solution

For current $J=aP-\kappa\nabla P/2$, a scalar potential exists when the one-form $\kappa^{-1}a$ is exact. Then $D=\kappa/2$, $a=-D\nabla V$, and $J=-PD\nabla(V+\log P)$.


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 Incoming links: Potential condition for a Fokker--Planck equation