  In the dynamics of open quantum systems, the backflow of information to the
reduced system under study has been suggested as the actual physical mechanism
inducing memory and thus leading to non-Markovian quantum dynamics. To this
aim, the trace-distance or Bures-distance revivals between distinct evolved
system states have been shown to be subordinated to the establishment of
system-environment correlations or changes in the environmental state. We show
that this interpretation can be substantiated also for a class of entropic
quantifiers. We exploit a suitably regularized version of Umegaki's quantum
relative entropy, known as telescopic relative entropy, that is tightly
connected to the quantum Jensen-Shannon divergence. In particular, we derive
general upper bounds on the telescopic relative entropy revivals conditioned
and determined by the formation of correlations and changes in the environment.
We illustrate our findings by means of examples, considering the
Jaynes-Cummings model and a two-qubit dynamics.
