  We compare dynamical heterogeneities in equilibrated supercooled liquids and
in the nonequilibrium glassy state within the framework of the random first
order transition theory. Fluctuating mobility generation and transport in the
glass are treated by numerically solving stochastic continuum equations for
mobility and fictive temperature fields that arise from an extended mode
coupling theory containing activated events. Fluctuating spatiotemporal
structures in aging and rejuvenating glasses lead to dynamical heterogeneity in
glasses with characteristics distinct from those found in the equilibrium
supercooled liquid. The non-Gaussian distribution of activation free energies,
the stretching exponent $\beta$, and the growth of characteristic lengths are
studied along with the four-point correlation function. Asymmetric
thermodynamic responses upon heating and cooling are predicted to be the
results of the heterogeneity and the out-of-equilibrium behavior of glasses
below $T_g$. Numerical results agree with experimental calorimetry. We
numerically confirm the prediction of Lubchenko and Wolynes in the glass that
the dynamical heterogeneity can lead to noticeably bimodal distributions of
local fictive temperatures which explains in a unified way recent experimental
observations that have been interpreted as coming from two distinct
equilibration mechanisms in glasses.
