  We analyze the dynamics of a system qudit of dimension mu sequentially
interacting with the nu-dimensional qudits of a chain playing the ore of an
environment. Each pairwise collision has been modeled as a random unitary
transformation. The relaxation to equilibrium of the purity of the system
qudit, averaged over random collisions, is analytically computed by means of a
Markov chain approach. In particular, we show that the steady state is the one
corresponding to the steady state for random collisions with a single
environment qudit of effective dimension nu_e=nu*mu. Finally, we numerically
investigate aspects of the entanglement dynamics for qubits (mu=nu=2) and show
that random unitary collisions can create multipartite entanglement between the
system qudit and the qudits of the chain.
