Fokker-Planck:
Probability Flow
Potential:
Harmonic V=x²/2
Double well V=x⁴/4−x²/2
Linear drift
Periodic V=sin(x)
Free diffusion
Diffusion D
0.50
Drift strength μ
1.00
Initial width σ₀
0.30
Reset
Pause
Fokker-Planck:
∂P/∂t = −∂[μ(x)P]/∂x + D·∂²P/∂x²
Describes probability density P(x,t) of a Langevin particle: ẋ = −V'(x) + √(2D) η(t).
Stationary solution:
P
st
(x) ∝ exp(−V(x)/D) — Boltzmann distribution with temperature D.
Color = log(P). Watch probability flow toward potential minima.