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Atomistic simulations with methods such as molecular dynamics are extremelypowerful tools to understand nanoscale dynamical behavior. The resultingtrajectories, by the virtue of being embedded in a high-dimensionalconfiguration space, can however be difficult to analyze and interpret. Thismakes low-dimensional representations, especially in terms of discrete jumpprocesses, extremely valuable. This simplicity however usually comes at thecost of accuracy, as tractable representations often entail simplifyingassumptions that are not guaranteed to be realized in practice. In this paper,we describe a discretization scheme for continuous trajectories that enables anarbitrarily accurate representation in terms of a Markov Renewal Process over adiscrete state space. The accuracy of the model converges exponentially fast asa function of a continuous parameter that has the interpretation of a localcorrelation time of the dynamics.

Arbitrarily accurate representation of atomistic dynamics via Markov Renewal Processes