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We examine theoretical and computational approaches that use fragments of Molecular Dynamic trajectories to compute kinetic and thermodynamic properties of complex systems. The trajectory fragments replace a single long trajectory that is widely used for these problems. We discuss the theories, approximations, and computational implementations, and why trajectory fragments lead to more efficient calculations. We further provide a numerical example (a transition in the Mueller potential) for the methods of Milestoning and Forward Flux, which exploit trajectory fragments differently. Advantages and disadvantages of the different approaches that use fragments and of the single trajectory calculations are discussed.

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