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Path reweighting is a principally exact method to estimate dynamic propertiesfrom biased simulations - provided that the path probability ratio matches thestochastic integrator used in the simulation. Previously reported pathprobability ratios match the Euler-Maruyama scheme for overdamped Langevindynamics. Since MD simulations use Langevin dynamics rather than overdampedLangevin dynamics, this severely impedes the application of path reweightingmethods. Here, we derive the path probability ratio $M_L$ for Langevin dynamicspropagated by a variant of the Langevin Leapfrog integrator. This new pathprobability ratio allows for exact reweighting of Langevin dynamics propagatedby this integrator. We also show that a previously derived approximate pathprobability ratio $M_{\mathrm{approx}}$ differs from the exact $M_L$ only by$\mathcal{O}(\xi^4\Delta t^4)$, and thus yields highly accurate dynamicreweighting results. ($\Delta t$ is the integration time step, $\xi$ is thecollision rate.) The results are tested and the efficiency of path-reweightingis explored using butane as an example.

Path probability ratios for Langevin dynamics -- exact and approximate