Random activation energy model and disordered kinetics, from static to dynamic disorder.

We suggest a unified path integral approach for random rate processes with random energy barriers, which includes systems with static and dynamic disorder as particular cases. We assume that the random component of the activation energy barrier can be described by a generalized Zubarev-McLennan nonequilibrum statistical ensemble that can be derived from the maximum information entropy approach by assuming that the time history of the fluctuations of the random components of the energy barrier are known. We show that the average survival function, which is an experimental observable in disorderd kinetics, can be computed exactly in terms of the characteristic functional of this generalized Zubarev-McLennan nonequilibrium statistical ensemble. We investigate different types of disorder described by our approach, ranging from static disorder with infinite memory to random processes with long or short memory, and finally to rapidly fluctuating independent random processes with no memory. We derive expressions of the average survival function for all these types of disorder and discuss their implications in the evaluation of kinetic parameters from experimental data. We illustrate our approach by studying a simple model of dynamic disorder of the renewal type. Finally we discuss briefly the implications of our approach in molecular biology and genetics.