  Entropy, and its temporal evolution, play a central role in the foundations
of quantum theory and in modern quantum technologies. Here we study, in
particular, the relations between the --- in general, non-Markovian ---
evolution of an open quantum system, the notions of divisibility of a dynamical
map and of distinguishability of quantum states, and the temporal behaviour of
various entropy-related quantities such as the Renyi (and sandwiched Renyi)
divergences, and the so-called min- and max- conditional entropies. This, in
turn, gives rise to an operational meaning of (non-)Markovianity.
