  In this paper we study the four point correlation function $\chi_4$ of
collective density fluctuations in a nonequilibrium liquid. The equilibration
is controlled by a modified stretched exponential behavior ( $\exp
[-{(t_\mathrm{w}/\tau)}^\beta]$ ) having the relaxation time $\tau$ dependent
on the aging time $t_\mathrm{w}$. Similar aging behavior has been seen
experimentally in supercooled liquids. The basic equations of fluctuating
nonlinear hydrodynamics (FNH) are solved here numerically to obtain $\chi_4$
for equilibrium and non equilibrium states. We also identify a dynamic length
scale $\xi$ from the equilibrated function. $\xi(T)$ grows with fall of
temperature $T$. From a broader perspective, we demonstrate here that the
characteristic signatures of dynamical heterogeneities in a supercooled liquid,
observed previously in computer simulations of the dynamics of a small number
of particles, are also present in the coarse grained equations of generalized
hydrodynamics.
