  We present an experimental study of the energy-relaxation in
Anderson-insulating indium-oxide films excited far from equilibrium. In
particular, we focus on the effects of history on the relaxation of the excess
conductance dG. The natural relaxation law of dG is logarithmic, namely
dG=-log(t). This may be observed over more than five decades following, for
example, cool-quenching the sample from high temperatures. On the other hand,
when the system is excited from a state S_{o} in which it has not fully reached
equilibrium to a state S_{n}, the ensuing relaxation law is logarithmic only
over time t shorter than the time t_{w} it spent in S_{o}. For times t>t_{w}
dG(t) show systematic deviation from the logarithmic dependence. It was
previously shown that when the energy imparted to the system in the excitation
process is small, this leads to dG=P(t/t_{w}) (simple-aging). Here we test the
conjecture that `simple-aging' is related to a symmetry in the relaxation
dynamics in S_{o} and S_{n}. This is done by using a new experimental procedure
that is more sensitive to deviations in the relaxation dynamics. It is shown
that simple-aging may still be obeyed (albeit with a modified P(t/t_{w})) even
when the symmetry of relaxation in S_{o} and S_{n} is perturbed by a certain
degree. The implications of these findings to the question of aging, and the
energy scale associated with correlations are discussed.
