Modeling and Simulation Group Meeting

A standard method to compute transport coefficients is to simulate the microscopic dynamics perturbed by a small non-equilibrium forcing up to a time $T$, time-average a desired observable over the trajectory, and the divide by the magnitude of the forcing, $\eta << 1$. Unfortunately, this method suffers from large finite-time sampling bias and variance in the limit of small forcing—on the order of $(T\eta)^{-1}$ and $(T\eta^2)^{-1}$ respectively.

For dynamics given by an SDE with additive elliptic noise, we propose a control variate approach using a sticky coupled version of the unperturbed dynamics. We show that when the drift is strongly contractive at infinity, this sticky coupling based estimator’s reduces the bias and variance by a factor of $\eta^{-1}$ compared to the standard method. Our hypotheses includes systems commonly used in molecular dynamics such as overdamped Langevin dynamics with Lennard-Jones interaction potential and quadratic confining potential.