  We study the thermalization of an ensemble of $N$ elementary,
arbitrarily-complex, quantum systems, mutually noninteracting but coupled as
electric or magnetic dipoles to a blackbody radiation. The elementary systems
can be all the same or belong to different species, distinguishable or
indistinguishable, located at fixed positions or having translational degrees
of freedom. Even if the energy spectra of the constituent systems are
nondegenerate, as we suppose, the ensemble unavoidably presents degeneracies of
the energy levels and/or of the energy gaps. We show that, due to these
degeneracies, a thermalization analysis performed by the popular quantum
optical master equation reveals a number of serious pathologies, possibly
including a lack of ergodicity. On the other hand, a consistent thermalization
scenario is obtained by introducing a Lindblad-based approach, in which the
Lindblad operators, instead of being derived from a microscopic calculation,
are established as the elements of an operatorial basis with squared amplitudes
fixed by imposing a detailed balance condition and requiring their
correspondence with the dipole transition rates evaluated under the first-order
perturbation theory. Due to the above-mentioned degeneracies, this procedure
suffers a basis arbitrariness which, however, can be removed by exploiting the
fact that the thermalization of an ensemble of noninteracting systems cannot
depend on the ensemble size. As a result, we provide a clear-cut partitioning
of the thermalization time into dissipation and decoherence times, for which we
derive formulas giving the dependence on the energy levels of the elementary
systems, the size $N$ of the ensemble, and the temperature of the blackbody
radiation.
