Rate Description of Markov Processes with Time Dependent Parameters∗

The description of physical, chemical or biological processes by simple models often becomes possible by a separation of time scales of the underlying microscopic dynamics [1,2]. For example, thermally activated transitions between locally stable states typically occur on a much slower time scale than the fast motion in the vicinity of these locally stable states [3]. On the long time scales on which the transitions occur, the fast dynamics leads to a complete loss of memory. Therefore, the escape from a locally stable state is characterized by a single total rate which in general is the sum of individual rates describing transitions into those states that can be reached