  We consider a non-interacting bipartite quantum system $\mathcal
H_S^A\otimes\mathcal H_S^B$ undergoing repeated quantum interactions with an
environment modeled by a chain of independant quantum systems interacting one
after the other with the bipartite system. The interactions are made so that
the pieces of environment interact first with $\mathcal H_S^A$ and then with
$\mathcal H_S^B$. Even though the bipartite systems are not interacting, the
interactions with the environment create an entanglement. We show that, in the
limit of short interaction times, the environment creates an effective
interaction Hamiltonian between the two systems. This interaction Hamiltonian
is explicitly computed and we show that it keeps track of the order of the
successive interactions with $\mathcal H_S^A$ and $\mathcal H_S^B$. Particular
physical models are studied, where the evolution of the entanglement can be
explicitly computed. We also show the property of return of equilibrium and
thermalization for a family of examples.
