  To describe short-time (picosecond) and small-scale (nanometre) transport in
fluids, a Green's function approach was recently developed. This approach
relies on an expansion of the distribution of single particle displacements
around a Gaussian function, yielding an infinite series of correction terms.
Applying a recent theorem [Van Zon and Cohen, J. Stat. Phys. 123, 1-37 (2006)]
shows that for sufficiently small times the terms in this series become
successively smaller, so that truncating the series near or at the Gaussian
level might provide a good approximation. In the present paper, we derive a
theoretical estimate for the time scale at which truncating the series at or
near the Gaussian level could be supposed to be accurate for equilibrium
nanoscale systems. In order to numerically estimate this time scale, the
coefficients for the first few terms in the series are determined in computer
simulations for a Lennard-Jones fluid, an isotopic Lennard-Jones mixture and a
suspension of a Lennard-Jones-based model of nanoparticles in a Lennard-Jones
fluid. The results suggest that for Lennard-Jones fluids an expansion around a
Gaussian is accurate at time scales up to a picosecond, while for nanoparticles
in suspension (a nanofluid), the characteristic time scale up to which the
Gaussian is accurate becomes of the order of five to ten picoseconds.
