Kramers Escape Rate & Thermal Activation

Brownian particle escaping an energy well — Arrhenius & Kramers rate theory
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1.20
1.0
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20
Escaped: 0
Rate (measured): --
Kramers rate: --
Arrhenius: --
Mean escape time: --

Physics

The Kramers escape rate: k = (ω_min·ω_max)/(2πγ) · exp(-ΔE/k_BT), where ω_min and ω_max are curvatures at the well and barrier, and γ is the damping. This generalizes the Arrhenius law k ∝ exp(-ΔE/k_BT) by including the pre-exponential (attempt frequency). Temperature controls the exponential — doubling ΔE or halving T reduces the rate exponentially. Applications: chemical reaction rates, protein folding, nucleation, neural spike timing.