We study the entanglement dynamics and relaxation properties of a system of two interacting qubits in the two cases (I) two independent bosonic baths and (II) one common bath, at temperature T. The entanglement dynamics is studied in terms of the concurrence C (t) between the two spins and of the von Neumann entropy S(t) with respect to the bath, as a function of time. We prove that the system does thermalize. In the case (II) of a single bath, the existence of a decoherence-free (DFS) subspace makes entanglement dynamics very rich. We show that when the system is initially in a state with a component in the DFS the relaxation time is surprisingly long, showing the existence of semi-decoherence free subspaces. The equilibrium state in this case is not the Gibbs state. The entanglement dynamics for the single bath case is also studied as a function of temperature, coupling strength with the environment and strength of tunneling coupling. The case of the mixed state is finally shown and discussed.
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