Peering into the crystal ball: Excess entropy scaling predicts equilibrium transport coefficients before equilibration

In a molecular-dynamics simulation, an equilibrium transport coefficient is to be computed (as the name suggests) in a system that has reached thermodynamic equilibrium. Indeed, the two most common methods for computing equilibrium transport coefficients-using the Einstein-Helfand (EH) relation and using the Green-Kubo (GK) relation-make the formal assumption that a system has reached thermodynamic equilibrium before sampling begins. There is, however, "no free lunch": Equilibration always demands an upfront computational investment. In this work, we study the question of just how much equilibration is needed for each computational method to yield a serviceable estimate for a transport coefficient, using as our case study a simple fluid that is initialized far out of configurational equilibrium. We show that a third method for computing transport coefficients-excess entropy scaling, which makes use of system structure in the form of the radial distribution function-has several statistically beneficial properties as compared to EH and GK, including faster convergence to the long-time-average value of the transport coefficient and lower sample-to-sample variance en route to convergence, which we rationalize from an information-theoretic perspective. Overall, this work points to the significant value that structure-based estimators may bring to any workflow demanding high-throughput calculation of transport coefficients.