  Magnetohydrodynamics (MHD) turbulence can drive significant temperature
fluctuations in the accretion disk of an active galactic nucleus (AGN). As a
result, the disk can be highly inhomogeneous and has a half-light radius larger
than the static Shakura \& Sunyaev Disk (SSD), in agreement with quasar
microlensing observations. Meanwhile, the accretion-disk sizes can also be
determined using continuum reverberation mappings which measure interband cross
correlations and time lags. The interband time lags are often understood in the
X-ray reprocessing scenario. Here we show that the interband continuum time
lags of the X-ray reprocessing of an inhomogeneous disk are similar to or even
smaller than those of a static SSD. Consequently, the X-ray reprocessing of an
inhomogeneous disk cannot account for the recent continuum reverberation
mappings of some Seyfert 1 AGNs, whose measured time lags are larger than those
of a static SSD. In contrast to the tight correlation between UV/optical
variations, the cross correlation between X-ray and disk emission is rather
weak in this model; this behavior is consistent with recent continuum
reverberation mappings. Moreover, the time lags in this model are
anti-correlated with the amplitude of disk temperature fluctuations. Our
results suggest that the temperature fluctuations should be properly considered
when modeling interband continuum time lags.
