= Solution
For constant isotropic diffusion and detailed balance, the drift has gradient form
$$
a=-M\nabla V
$$
for 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,
$$
\dot\phi=-a=M\nabla V.
$$
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.
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