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Position-dependent memory kernel in generalized Langevin equations: theory and numerical estimation (2201.02457v3)

Published 7 Jan 2022 in cond-mat.stat-mech, physics.chem-ph, and physics.comp-ph

Abstract: Generalized Langevin equations with non-linear forces and position-dependent linear friction memory kernels, such as commonly used to describe the effective dynamics of coarse-grained variables in molecular dynamics, are rigorously derived within the Mori-Zwanzig formalism. A fluctuation-dissipation theorem relating the properties of the noise to the memory kernel is shown. The derivation also yields Volterra-type equations for the kernel, which can be used for a numerical parametrization of the model from all-atom simulations.

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