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Timescales for stochastic barrier crossing: Inferring the potential from nonequilibrium data.

A J Archer¹, T Ala-Nissila^1,2, T J W Honour³

¹Department of Mathematical Sciences and Interdisciplinary Centre for Mathematical Modelling, Loughborough University, Loughborough LE11 3TU, United Kingdom.

The Journal of Chemical Physics

|August 11, 2025

Summary

Kramers's rate theory misses early-time dynamics. This study reveals key nonequilibrium timescales and potential landscape formation in barrier crossing, crucial for understanding activated processes at finite times.

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Area of Science:

Chemical Physics
Statistical Mechanics
Physical Chemistry

Background:

Kramers's rate theory is foundational for barrier crossing but limited to equilibrium conditions.
Early-time, nonequilibrium dynamics are crucial for understanding activated processes but are often excluded.

Purpose of the Study:

To investigate early-time nonequilibrium dynamics in a barrier-crossing model.
To identify and quantify key timescales governing nonequilibrium behavior.
To explore the construction of potential landscapes from dynamic data.

Main Methods:

Utilized the Smoluchowski equation (SE) and stochastic path integral (SPI) mapping.
Analyzed a model system of overdamped particle dynamics in a double-well potential.
Calculated the current at the barrier for bistable and asymmetric potentials.

Main Results:

Identified distinct timescales for well equilibration, effective potential inflexion, and second well emergence.
Observed that the timescale for second well inference decreases with increasing barrier height.
Found significant deviations from equilibrium predictions at early times (t ≪ τB).
Determined that the crossover time to equilibrium rate theory is barrier height independent.

Conclusions:

Early-time dynamics deviate significantly from equilibrium predictions.
Accurate potential landscape construction requires sufficient sampling time (t ≫ τB).
Results offer insights into controlling activated processes at finite times.