Γ-Limit for Transition Paths of Maximal Probability

Chemical reactions can be modeled 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 Γ-limit of this functional is determined explicitly in the case where the temperature is small and the transition time scales as the inverse temperature.