  The time-dependence of the quantum entropy for a two-level atom interacting
with a single-cavity mode is computed using the Jaynes-Cummings model, when the
initial state of the radiation field is prepared in a thermal state with
temperature fluctuations. In order to describe the out-of-equilibrium
situation, the Super Statistics approximation is implemented so that the gamma
and the multi-level distribution functions are used to introduce the inverse
temperature fluctuations. In the case of the gamma distribution, paralleling
the Tsallis non-additive formalism, the entropy for the system is computed with
the $q$-logarithm prescription, and the impact of the initial state of the atom
is also taken into account. The results show that, in the first distribution,
the $q$-parameter (related to the thermal fluctuations) modifies the partial
entropies appreciably. In contrast, the way the inverse temperatures are
distributed in the second one may lead to changes in the entropy functions.
