  We discuss how the thermalization of an elementary quantum system is modified
when the system is placed in an environment out of thermal equilibrium. To this
aim we provide a detailed investigation of the dynamics of an atomic system
placed close to a body of arbitrary geometry and dielectric permittivity, whose
temperature $T_M$ is different from that of the surrounding walls $T_W$. A
suitable master equation for the general case of an $N$-level atom is first
derived and then specialized to the cases of a two- and three-level atom.
Transition rates and steady states are explicitly expressed as a function of
the scattering matrices of the body and become both qualitatively and
quantitatively different from the case of radiation at thermal equilibrium. Out
of equilibrium, the system steady state depends on the system-body distance, on
the geometry of the body and on the interplay of all such parameters with the
body optical resonances. While a two-level atom tends toward a thermal state,
this is not the case already in the presence of three atomic levels. This
peculiar behavior can be exploited, for example, to invert the populations
ordering and to provide an efficient cooling mechanism for the internal state
of the quantum system. We finally provide numerical studies and asymptotic
expressions when the body is a slab of finite thickness. Our predictions can be
relevant for a wide class of experimental configurations out of thermal
equilibrium involving different physical realizations of two or three-level
systems.
