WHAT MAKES MOLECULAR DYNAMICS WORK?

The equations of motion for deterministic molecular dynamics (MD) are chaotic, creating problems for their numerical treatment due to the exponential growth of error with time. Indeed, modeling and computational errors overwhelm numerical trajectories in typical simulations. Consequently, accuracy is expected only in a statistical sense, based on random initial conditions. Of great interest then is the relationship between errors in the dynamics and their effects on the accuracy of statistical quantities, specifically, expectations. This article provides a formula for the effect of a perturbation on an ensemble average, which explains the accuracy of such calculations. It also provides a formula for the effect of a perturbation on a time correlation function, which, however, fails to explain accuracy for these calculations. Additionally, this article clarifies the relationships among various dynamical properties of MD and provides an extension to a theory of non-Hamiltonian MD.