The Derivation and Approximation of Coarse-grained Dynamics from Langevin Dynamics
This work provides a theoretical framework for coarse-graining in molecular dynamics, but the results are incremental and lack concrete numerical validation.
The authors derive a coarse-grained model from Langevin dynamics, focusing on the memory kernel and fluctuation-dissipation theorem, and present a hierarchy of approximations that eliminate the need to evaluate the memory integral at each time step, offering increasing accuracy.
We present a derivation of a coarse-grained model from the Langevin dynamics. The focus is placed on the memory kernel function and the fluctuation-dissipation theorem. Also presented is an hierarchy of approximations for the memory and random noise terms, using rational approximations in the Laplace domain. These approximations offer increasing accuracy. More importantly, they eliminate the need to evaluate the integral associated with the memory term at each time step.