Fokker-Planck Equation

The Fokker-Planck PDE governs the evolution of probability density P(x,t) for a stochastic process dx = A(x)dt + D·dW. Equilibrium is the Boltzmann distribution e^{−V/D}.

∂P/∂t = −∂[A(x)P]/∂x + D ∂²P/∂x²
A(x) = −V'(x) (drift)
P_eq ∝ e^{−V(x)/D}
t = 0