  The effect of non-Newtonian rheology, manifested through a viscoelastic
linearized Maxwell model, on the time-dependent non-equilibrium concentration
fluctuations due to free diffusion as well as thermal diffusion of a species is
analyzed theoretically. The non-equilibrium process is quantified through the
concentration fluctuation auto-correlation function, also known as the dynamic
structure factor. The analysis reveals that the effect of rheology is prominent
for both the cases of free diffusion and thermal diffusion at long times where
the rheology dictates not only the location of the peaks in concentration
auto-correlations, but also the magnitudes; such peaks in the auto-correlation
function are absent in the case of a Newtonian fluid. At smaller times, for the
case of free diffusion presence of time-dependent peak(s) are observed, which
are weakly dependent on the influence of rheology, a phenomenon which is absent
in the case of thermal diffusion. Lastly, different regimes of the frequency
dependent overall dynamic structure factor depending on the interplay of the
fluid relaxation time and momentum diffusivity are evaluated.
