Generalized Langevin Equation: An Introductory Review for Biophysicists

Abstract

An introductory, pedagogical review of the generalized Langevin equation (GLE) within the classical regime is presented. It is intended to be accessible to biophysicists with an interest in molecular dynamics (MD).

Section 1 presents why the equation may be of interest within biophysical modeling. A detailed elementary first principles derivation of the (multidimensional) Kac–Zwanzig model is presented. The literature is reviewed with a focus on biophysical applications and representation by Markovian stochastic differential equations. The relationship with the Mori–Zwanzig formalism is discussed. The framework of model reduction and approximation is emphasized. Some open problems are identified. Show more