Barrier Crossing

Mean First Passage Time & Kramers Theory

Potential

Results

Kramers MFPT
Measured MFPT
Crossings
Rate k = 1/MFPT
Arrhenius exp(−ΔV/kT)
Kramers (1940): MFPT ≈ (2πγ/ω_min·ω_max) · exp(ΔV/kT). The exponential Boltzmann factor dominates — rate is exponentially sensitive to barrier height. Underdamped: oscillations in well matter. Overdamped: diffusion across barrier. The escape rate is the foundation of chemical kinetics, nucleation theory, and protein folding.