  We analyze the dynamics of a system qubit interacting by means a sequence of
pairwise collisions with an environment consisting of just two qubits. We show
that the density operator of the qubits approaches a common time averaged
equilibrium state, characterized by large fluctuations, only for a random
sequence of collisions. For a regular sequence of collisions the qubitstates of
the system and of the reservoir undergo instantaneous periodic oscillations and
do not relax to a common state. Furthermore we show that pure bipartite
entanglement is developed only when at least two qubits are initially in the
same purestate while otherwise also genuine multipartite entanglement builds
up.
