The Fokker-Planck equation ∂P/∂t = -∂/∂x[F(x)P] + D∂²P/∂x² governs how a probability density evolves under drift F(x) = -dV/dx and diffusion D. Watch the distribution relax toward the Boltzmann equilibrium P∞ ∝ exp(-V(x)/D).
Equilibrium (dashed) = Boltzmann distribution exp(-V/D). Blue = current P(x,t).