Out of Equilibrium, But Not Out of Mind: Rapid Estimation of Fluid Transport Coefficients in Molecular Simulations Away from Thermodynamic Equilibrium

Molecular-dynamics (MD) simulation is a widely used method for the study of fluids at the molecular scale. MD simulations are frequently used to predict, and understand fundamental mechanisms underlying, important fluid transport properties. But MD simulations never directly supply these (or in fact any) material properties; the only data directly supplied by an MD simulation are particle kinematics. A significant body of theory has been developed to convert particle kinematics into material properties of interest; as one example (of many), Green-Kubo theory can be used to convert particle velocities into a diffusion coefficient. All this well-established theory is formally valid in the infinite-time/infinite-statistics limit; in practice, one can only simulate a finite number of particles for a finite amount of time. In this talk, we investigate optimal strategies for estimating fluid transport coefficients in molecular simulations in this pre-asymptotic regime, with a focus on systems out of thermodynamic equilibrium. We show that a class of estimators, based upon excess entropy scaling, perform well in a range of practical (and even in some cases exotic) out-of-equilibrium conditions. We validate our results with MD simulations of a variety of simple and not-so-simple liquids.