  We compare two approaches to non-Markovian quantum evolution: one based on
the concept of divisible maps and the other one based on distinguishability of
quantum states. The former concept is fully characterized in terms of local
generator whereas it is in general not true for the latter one. A simple
example of random unitary dynamics of a qubit shows the intricate difference
between those approaches. Moreover, in this case both approaches are fully
characterized in terms of local decoherence rates. As a byproduct it is shown
that entropy might monotonically increase even for non-Markovian qubit
dynamics.
