  We use the AdS/CFT correspondence to study a thermally isolated conformal
field theory in four dimensions which undergoes a repeated deformation by an
external periodic time-dependent source coupled to an operator of dimension
Delta. The initial state of the theory is taken to be at a finite temperature.
We compute the energy dissipated in the system as a function of the frequency
and of the dimension Delta of the perturbing operator. This is done in the
linear response regime. In order to study the details of thermalization in the
dual field theory, the leading-order backreaction on the AdS black brane metric
is computed. The evolution of the event and the apparent horizons is monitored;
the increase of area in each cycle coincides with the increase in the
equilibrium entropy corresponding to the amount of energy dissipated. The time
evolution of the entanglement entropy of a spherical region and that of the
two-points function of a probe operator with a large dimension are also
inspected; we find a delay in the thermalization of these quantities which is
proportional to the size of the region which is being probed. Thus, the delay
is more pronounced in the infrared. We comment on a possible transition in the
time evolution of the energy fluctuations.
