  A simple model for variability in relativistic plasma outflows is studied, in
which nonthermal electrons are continuously and uniformly injected in the
comoving frame over a time interval dt. The evolution of the electron
distribution is assumed to be dominated by synchrotron losses, and the energy-
and time-dependence of the synchrotron and synchrotron self-Compton (SSC)
fluxes are calculated for a power-law electron injection function with index s
= 2. The mean time of a flare or pulse measured at photon energy E with respect
to the onset of the injection event varies as E^{-1/2} and E^{-1/4} for
synchrotron and SSC processes, respectively, until the time approaches the
limiting intrinsic mean time (1+z)dt/(2 D), where z is the redshift and D is
the Doppler factor. This dependence is in accord with recent analyses of blazar
and GRB emissions, and suggests a method to discriminate between external
Compton and SSC models of high-energy gamma radiation from blazars and GRBs.
The qualititative behavior of the X-ray spectral index/flux relation observed
from BL Lac objects can be explained with this model. This demonstrates that
synchrotron losses are primarily responsible for the X-ray variability behavior
and strengthens a new test for beaming from correlated hard X-ray/TeV
observations.
