title: The derivation and approximation of coarse-grained dynamics from Langevin dynamics.
abstract: We present a derivation of a coarse-grained description, in the form of a generalized Langevin equation, from the Langevin dynamics model that describes the dynamics of bio-molecules. The focus is placed on the form of the memory kernel function, the colored noise, and the second fluctuation-dissipation theorem that connects them. Also presented is a 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. Direct sampling of the colored noise can also be avoided within this framework. Therefore, the numerical implementation of the generalized Langevin equation is much more efficient.
authors.affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802-6400, USA.
authors.forename: Lina
authors.initials: L
authors.lastname: Ma
authors.affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802-6400, USA.
authors.forename: Xiantao
authors.initials: X
authors.lastname: Li
authors.affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802-6400, USA.
authors.forename: Chun
authors.initials: C
authors.lastname: Liu
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical; D025341:Principal Component Analysis