Potential condition for a Fokker--Planck equation
= Potential condition for a Fokker--Planck equation
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 $J=-PD\nabla(V+\log P)$.