Position-dependent memory kernel in generalized Langevin equations: Theory and numerical estimation

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. Published under an exclusive license by AIP Publishing.

Automated summary

This paper rigorously derives the generalized Langevin equations, which are commonly used to describe the effective dynamics of coarse-grained variables in molecular dynamics. These equations include non-linear forces and position-dependent linear friction memory kernels. The paper also presents a fluctuation-dissipation theorem that relates the properties of the noise to the memory kernel, as well as Volterra-type equations for the kernel that can be used for numerical parametrization of the model from all-atom simulations.