Equations of motion for non-equilibrium molecular dynamics simulations of viscous flow in molecular fluids

Abstract

Equations of motion are given that are suitable for setting up non-equilibrium momentum fluxes in molecular fluids. In a recent article Marechal and Ryckaert have pointed out that equilibrium time correlation functions depend on whether the stress is measured in a centre of mass or atomic representation. In non-equilibrium simulations of molecular systems, a corresponding ambiguity arises between perturbations applied to the individual atoms and perturbations applied to the centres-of-mass of the molecules. I use linear response theory to demonstrate the equivalence of the non-equilibrium equations of motion with the equilibrium correlation functions, for small strain rates. I also show that the two sets of equations of motion produce identical trajectories in the low-frequency limit. In this limit the equations of motion are equivalent to the Lees-Edward's method, but at finite frequencies the moving boundary method is incorrect.