Mean First-Passage Time & Kramers Escape

Thermal escape over potential barriers — Arrhenius law and prefactor

k = (ω₀·ω_b)/(2π) · e^−ΔU/k_BT | ⟨τ⟩ = 1/k (mean first passage time)
ω₀ = well frequency, ω_b = barrier frequency | ΔU = barrier height

Barrier height ΔU (in units of k_BT₀) = 3.0

Temperature T (in units of T₀) = 1.0

Well curvature ω₀ = 1.0

Barrier curvature ω_b = 0.8

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Escape rate k

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MFPT ⟨τ⟩

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ΔU/k_BT