On stochastic models of dynamic disorder.

In this paper we investigate some general aspects of stochastic models of dynamic disorder. First, we reexamine the Zwanzig model for the kinetics of escape through a fluctuating hole. We show that this model is trivially connected to the canonical model of the broadening of the zero-phonon line (ZPL) in crystals. This provides a new perspective of the Wang-Wolynes expression for the rate of escape from a geometric bottleneck with non-Markovian Gaussian fluctuations. Motivated by recent single-molecule experiments, we examine more general examples of fluctuation processes from the perspective of cumulant expansions. Finally, we discuss recent single-molecule experiments probing enzyme turnover performed by Xie and co-workers.