Kramers Escape Rate

τ ∝ exp(ΔU / kT) — thermal escape from a double-well potential

Barrier ΔU: 2.0 Temperature kT: 0.8

Kramers (1940): rate k ≈ (ω_min·ω_max / 2πγ) · e^{−ΔU/kT}. Right panel: Arrhenius plot of measured escape times vs 1/kT. Langevin dynamics: mẍ = −V'(x) − γẋ + √(2γkT) η(t).