  We study two types of intrinsic uncertainties, statistical errors and system
size effects, in estimating shear viscosity via equilibrium molecular dynamics
simulations and compare them with the corresponding uncertainties in evaluating
the self-diffusion coefficient. Uncertainty quantification formulas for the
statistical errors in the shear-stress autocorrelation function and shear
viscosity are obtained under the assumption that shear stress follows a
Gaussian process. Analyses of simulation results for simple and complex fluids
reveal that the Gaussianity is more pronounced in the shear-stress process
(related to shear viscosity estimation) compared with the velocity process of
an individual molecule (related to self-diffusion coefficient). At relatively
high densities corresponding to a liquid state, we observe that the shear
viscosity exhibits complex size-dependent behavior unless the system is larger
than a certain length scale, beyond which reliable shear viscosity values are
obtained without any noticeable scaling behavior with respect to the system
size. We verify that this size-dependent behavior is configurational and relate
the characteristic length scale to the shear-stress correlation length.
