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

Role of non-Markovianity and backflow of information in the speed of quantum evolution