Diffusive escape and reentry through a channel in the cavity wall

We show that the kinetics of diffusive escape from a cavity through a narrow channel in the cavity wall and successive reentry can be described by a formal kinetic scheme for reversible dissociation of a spherical binding site with appropriately defined effective association and dissociation rate constants. Initially the population of the cavity decays exponentially, with the rate constant determined by the cavity volume and the channel length and radius. A crossover to the universal inverse power law behavior, which does not depend on the channel geometry, occurs at long times. These simple predictions are in excellent agreement with the results of Brownian dynamics simulations.