A particle in a double-well potential escapes via thermal fluctuations. Kramers theory gives the mean first-passage time τ = (2πγ)/(ω_a·ω_b) · exp(ΔE/kT), where ω_a and ω_b are curvatures at the well and barrier.
Kramers (1940) solved the Fokker-Planck equation for escape over a potential barrier. The Arrhenius factor exp(−ΔE/kT) dominates: each kT of temperature multiplies the rate by e. The prefactor depends on potential curvatures ω = √|V''|. In the underdamped regime, the formula changes — here we show the overdamped (Smoluchowski) limit.