  The dynamics of a single qubit interacting by a sequence of pairwise
collisions with an environment consisting of just two more qubits is analyzed.
Each collision is modeled in terms of a random unitary operator with a uniform
probability distribution described by the uniform Haar measure. We show that
the purity of the system qubit as well as the bipartite and the tripartite
entanglement reach time averaged equilibrium values characterized by large
instantaneous fluctuations.These equilibrium values are independent of the
order of collision among the qubits. The relaxation to equilibrium is analyzed
also in terms of an ensemble average of random collision histories. Such
average allows for a quantitative evaluation and interpretation of the decay
constants. Furthermore a dependence of the transient dynamics on the initial
degree of entanglement between the environment qubits is shown to exist.
Finally the statistical properties of bipartite and tripartite entanglement are
analyzed.
