  We apply the DDC formalism [proposed by Dalibard, Dupont-Roc and
Cohen-Tannoudji] to study the average rate of change of energy of two identical
two-level atoms interacting with the vacuum massless scalar field in
synchronized motion along stationary trajectories. By separating the
contributions of vacuum fluctuations and atomic radiation reaction, we first
show that for the two-atom system initially prepared in the factorizable
eigenstates $|g_Ag_B\rangle$ and $|e_Ae_B\rangle$, where $g$ and $e$ represent
the ground state and the excited state of a single atom respectively, both
vacuum fluctuations and atomic radiation reaction contribute to the average
rate of change of energy of the two-atom system, and the contribution of vacuum
fluctuations is independent of the interatomic separation while that of atomic
radiation reaction is dependent on it. This is contrary to the existing results
in the literature where vacuum fluctuations are interatomic-separation
dependent. However, if the two-atom system is initially prepared in the
unfactorizable symmetric/antisymmetric entangled state, the average rate of
change of energy of the two-atom system is never perturbed by the vacuum
fluctuations, but is totally a result of the atomic radiation reaction. We then
consider two special cases of motion of the two-atom system which is initially
prepared in the symmetric/antisymmetric entangled state, i.e., synchronized
inertial motion and synchronized uniform acceleration. In contrast to the
average rate of change of energy of a single uniformly accelerated atom, the
average rate of change of energy of the uniformly accelerated two-atom system
is nonthermal-like. The effects of noninertial motion on the transitions of
states of the two correlated atoms are also discussed.
