 Probability current velocity

Where a probability density $\psi$ is positive, its Fokker-Planck probability current can be written $\mathbf{J}=\psi \mathbf{V}$, giving a continuity equation ${\partial }_t\psi +\nabla \cdot (\psi \mathbf{V})=0$. This velocity transports probability. It is not a differentiable instantaneous velocity of an overdamped Brownian motion path. In the Hookean dumbbell model, its osmotic term is $-(2k_{B}T/\zeta )\nabla \log \psi$.