  Modern methods of simulating molecular systems are based on the mathematical
theory of Markov operators with a focus on autonomous equilibrated systems.
However, non-autonomous physical systems or non-autonomous simulation processes
are becoming more and more important. We present a representation of
non-autonomous Markov jump processes as autonomous Markov chains on space-time.
Augmenting the spatial information of the embedded Markov chain by the temporal
information of the associated jump times, we derive the so-called augmented
jump chain. The augmented jump chain inherits the sparseness of the
infinitesimal generator of the original process and therefore provides a useful
tool for studying time-dependent dynamics even in high dimensions. We
furthermore discuss possible generalizations and applications to the
computation of committor functions and coherent sets in the non-autonomous
setting. After deriving the theoretical foundations we illustrate the concepts
with a proof-of-concept Galerkin discretization of the transfer operator of the
augmented jump chain applied to simple examples.
