The influence of diffusing diffusivity on barrier crossing dynamics

Abstract

This paper investigates how the conventional picture of condensed phase reaction dynamics—based on Kramers’ flux-over-population approach—is modified by the process of “diffusing diffusivity,” the mechanism generally understood to underlie the anomalous behavior of particles in cellular interiors and other complex liquids. The question is addressed here within the framework of a model in which a point particle evolves stochastically in a double-well potential in the presence of thermal fluctuations that are coupled multiplicatively to Ornstein–Uhlenbeck (O–U) noise. The model is used to calculate various measures of barrier crossing statistics, including the survival probability, the mean first passage time, and the mean first passage time distribution, for all of which exact expressions can be derived. It is also found that as a result of the influence of the O–U relaxation timescale on particle motion, these quantities become dynamically heterogeneous. Furthermore, in the disorder-free limit, they yield expressions that are quite different—in general appearance—from the corresponding formulas in Kramers’ analysis, but are still consistent with them nevertheless.