  We use the microscopic derivation of the Jaynes-Cummings model master
equation under field losses to study the dynamics of initial field states
beyond the single-excitation manifold. We show that field-qubit detuning, as
well as finite temperature, modify the effective decay rate in the model using
entropy measures, like qubit-field purity and von Neumann entropy of the field,
for initial Fock states. For initial semi-classical states of the field, we
show that the microscopic approach, in phase space, provides an evolution to
thermal equilibrium that is smoother than the one provided by the standard
phenomenological approach.
