Rare switching events in non-stationary systems

Physical systems with many degrees of freedom can often be understood in terms of transitions between a small number of metastable states. For time-homogeneous systems with short-term memory these transitions are fully characterized by a set of rate constants. We consider the question how to
extend such a coarse-grained description to non-stationary systems and to systems with finite memory. We identify the physical regimes in which time-dependent rates are meaningful, and state microscopic expressions that can be used to measure both externally time-dependent and history-dependent rates in microscopic simulations. Our description can be used to generalize Markov state models to time-dependent Markovian or non-Markovian systems.