  A Markov approximation in open quantum dynamics can give unphysical results
when a map acts on a state that is not in its domain. This is examined here in
a simple example, an open quantum dynamics for one qubit in a system of two
interacting qubits, for which the map domains have been described quite
completely. A time interval is split into two parts and the map from the exact
dynamics for the entire interval is replaced by the conjunction of that same
map for both parts. If there is any correlation between the two qubits,
unphysical results can appear as soon as the map conjunction is used, even for
infinitesimal times. If the map is repeated an unlimited number of times, every
state is at risk of being taken outside the bounds of physical meaning.
Treatment by slippage of initial conditions is discussed.
