Evolution equations for open systems and collective variables: Which equation would you like to solve by molecular dynamics simulation?

Abstract

In molecular dynamics simulations, the Langevin equation is frequently used to model the dynamics of collective variables and of systems coupled to baths. Often, external forces are added to the Langevin equation (e.g., when using targeted or steered molecular dynamics in biomolecular simulation). It is also popular to add derivatives of thermodynamic potentials to the Langevin equation as effective forces (e.g., when using a potential of mean force in a coarse-grained polymer model). These practices can be adventurous. In this article, we recall derivations of different versions of the Langevin equation and we discuss why care is needed if one would like to make changes to the structure of the equation.