Dynamical reweighting for estimation of fluctuation formulas

We propose a variance reduction method for calculating transport coefficients in molecular dynamics using an importance sampling method via Girsanov's theorem applied to Green--Kubo's formula. We optimize the magnitude of the perturbation applied to the reference dynamics by means of a scalar parameter~$\alpha$ and propose an asymptotic analysis to fully characterize the long-time behavior in order to evaluate the possible variance reduction. Theoretical results corroborated by numerical results show that this method allows for some reduction in variance, although rather modest in most situations.