Markovianity criteria for quantum evolution
  We characterize a class of Markovian dynamics using the concept of divisible dynamical map. Moreover we provide a family of criteria which can distinguish Markovian and non-Markovian dynamics. These Markovianity criteria are based on a simple observation that Markovian dynamics implies monotonic behavior of several well known quantities like distinguishability of states, fidelity, relative entropy and genuine entanglement measures. 
Dariusz Chru\'sci\'nski, Andrzej Kossakowski
quant-ph math-ph math.MP