  We investigate a system of two interacting qubits having one of them isolated
and the other coupled to a thermal reservoir. We consider two different models
of system-reservoir interaction: i) a "microscopic" model, in which the master
equation is derived taking into account the interaction between the two
subsystems (qubits), ii) a naive "phenomenological" model, in which the master
equation consists of a dissipative term added to the unitary evolution term. We
study the dynamics of quantities such as bipartite entanglement, quantum
discord and the linear entropy of the isolated qubit for both strong and weak
coupling regimes (qubit-qubit interaction) as well as for different
temperatures of the reservoir. We find significant disagreements between the
results obtained from the two models even in the weak coupling regime. For
instance, we show that according to the phenomenological model, the isolated
qubit would approach a maximally mixed state more slowly for higher
temperatures (unphysical result), while the microscopic model predicts the
opposite behaviour (correct result).
