Mass transport computations via correlation splitting and a law of total diffusion

Directly computing mass transport coefficients in stochastic models requires integrating over time the equilibrium correlations between atomic displacements. Here, we show how to accelerate the computations via \green{correlation splitting and conditioning, which statistically amounts to estimating the mass transport coefficients} through a law of total diffusion. We illustrate the approach with kinetic path sampling simulations of atomic diffusion in a \green{random alloy model} in which percolating solute clusters trap the mediating vacancy. There, Green functions serve to generate first-passage paths escaping the traps and to propagate the long-time dynamics. When they also serve to estimate mean-squared displacements via conditioning, colossal reductions of statistical \green{errors} are achieved.