On the estimation and correction of discretization error in molecular dynamics averages

The computation of statistical averages is one of the most important applications of molecular dynamics simulation, allowing for the estimation of macroscopic physical quantities through averages of observables sampled along microscopic trajectories. In this article, we investigate the impact of discretization error on the accuracy of molecular dynamics averages. Given a Hamiltonian system and a symplectic integrator, new weighting methods are derived to better approximate averages of certain observables, without changing the system or integrator. These new methods are shown to reduce discretization error and enhance the order of accuracy without high-overhead calculations.