Kramers' Escape — Mean First Passage Time

Kramers (1940): mean first passage time from well bottom to barrier top in a 1D potential V(x) follows MFPT ≈ (2π/ω_a·ω_b) · exp(ΔU/D), where ΔU = V_max − V_min is the barrier height and D is the diffusion coefficient. This Arrhenius law means exponentially rare escape events. Click on the potential canvas to place the potential minimum. The Arrhenius plot shows log(MFPT) vs 1/D. Exit time distribution is approximately exponential (memoryless process).