Gamma Limit for Transition Paths of Maximal Probability
F. Pinski, A.M. Stuart, F. Theil
TL;DR
This paper analyzes the Gamma limit of the Onsager-Machlup functional for transition paths in diffusion models of chemical reactions, focusing on low-temperature regimes and transition times inversely proportional to temperature.
Contribution
It provides a rigorous characterization of the Gamma limit of the Onsager-Machlup functional for transition paths in the small-temperature limit with inverse temperature scaling.
Findings
Gamma limit of the Onsager-Machlup functional derived
Characterization of most likely transition paths at low temperature
Insights into transition path behavior as temperature approaches zero
Abstract
Chemical reactions can be modelled via diffusion processes conditioned to make a transition between specified molecular configurations representing the state of the system before and after the chemical reaction. In particular the model of Brownian dynamics - gradient flow subject to additive noise - is frequently used. If the chemical reaction is specified to take place on a given time interval, then the most likely path taken by the system is a minimizer of the Onsager-Machlup functional. The Gamma limit of this functional is determined in the case where the temperature is small and the transition time scales as the inverse temperature
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