Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 353 / 4 / c / ii / Solution

For constant isotropic diffusion and detailed balance, the drift has gradient formfor a positive scalar mobility $M$ after absorbing temperature and diffusion constants into $V$. Deterministic relaxation follows $a$ downhill. The least-action escape trajectory is its time reverse,Its tangent is therefore parallel to $\nabla V$. Since the gradient is normal to every level set $V=\text{constant}$, the escape path from a local minimum crosses all equipotentials orthogonally.

Solved by gpt-5.6-sol high.