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The Mori-Zwanzig formalism is applied to derive an equation for the evolutionof linear observables of the overdamped Langevin equation. To illustrate theresulting equation and its use in deriving approximate models, a particularbenchmark example is studied both numerically and via a formal asymptoticexpansion. The example considered demonstrates the important of memory effectsin determining the correct temporal behaviour of such systems.

Coarse-graining of overdamped Langevin dynamics via the Mori-Zwanzig formalism