Kramers Escape Problem

Thermal activation over a double-well potential — Arrhenius rate r = ν₀ exp(−ΔU/k_BT)

Parameters

Live Statistics

Position x:
Current well:
Escapes (left→right): 0
Escapes (right→left): 0
Predicted Arrhenius rate:
Time in simulation: 0

Kramers Theory

Kramers (1940): escape rate over a barrier of height ΔU at temperature T:

k = (ω₀ ω_b)/(2πγ) · exp(−ΔU/k_BT)

where ω₀ = curvature at well bottom, ω_b = curvature at barrier top, γ = damping. Generalized Arrhenius: rate is exponentially suppressed by barrier relative to thermal energy. Basis of chemical reaction rate theory.