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.
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.
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