  It is known that the time evolution of a subsystem from an initial state to
two later times, t1, t2 (t2 > t1), are both completely positive (CP) but it is
shown here that in the intermediate times between t1 and t2, in general, it
need not be CP. This reveals the key to the Markov (if CP) and nonMarkov (if
NCP) avataras of the intermediate dynamics. This is brought out based on A and
B dynamical maps - without resorting to Master equation approach. The choice of
tensor product form for the global initial state points towards the
system-environment interaction dynamics as the sole cause for
Markovianity/non-Markovianity. A succinct summary of the results is given in
the form of a table.
