Path probability ratios for Langevin dynamics—Exact and approximate

Path reweighting is a principally exact method to estimate dynamic properties from biased simulations—provided that the path probability ratio matches stochastic integrator used in simulation. Previously reported ratios match Euler–Maruyama scheme for overdamped Langevin dynamics. Since molecular dynamics simulations use rather than dynamics, this severely impedes application of methods. Here, we derive ML propagated by variant Leapfrog integrator. This new allows We also show previously derived approximate Mapprox differs only O(?4?t4) and thus yields highly accurate results. (?t integration time step, ? collision rate.) The results are tested, efficiency explored using butane as an example.