  We consider a two-level open quantum system undergoing either pure dephasing,
dissipative, or multiply decohering dynamics and show that, whenever the
dynamics is non-Markovian, the initial speed of evolution is a monotonic
function of the relevant physical parameter driving the transition between the
Markovian and non-Markovian behaviour of the dynamics. In particular, within
the considered models, a speed increase can only be observed in the presence of
backflow of information from the environment to the system.
