Generalized Langevin equations for molecular dynamics in solution

Abstract

This paper rigorously derives several classes of generalized Langevin equations (GLE) which describe the motion of an interacting many-body system in a heat bath. The fundamental assumption in deriving these GLEs is that the Liouville operator representing the system–heat bath interaction LSR commutes with the global Liouville operator L. An important second dissipation–fluctuation theorem is put forward relating the memory kernel of the friction force to the correlation function between the potential force of the system and the random force from the heat bath and to the auto- and cross-correlation functions of the random forces. Unlike most of the previous treatments in which the system, the heat bath and the system–heat bath interaction are greatly simplified, the properties of the system, the heat bath and the system–heat bath interaction remain general in this study. In particular, the interaction Hamiltonian may be arbitrarily nonlinear, so that the present theory is applicable to any physical system. Finally, a unified treatment for the GLEs, originally proposed by Ciccotti and Ryckaert for the systems in which there is no interaction among particles, is extended to many-body systems with internal interactions and in a heat bath.