Entropy exchange and thermal fluctuations in Jaynes-Cummings model

The time-dependence of the quantum entropy for a two-level atom interacting with a single-cavity mode is computed by 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. By making a parallelism with the Tsallis non-additive formalism, the entropy for the field is computed with the $q$-logarithm prescription, so that the entropy of the whole system is a mixture of the von-Neumman (for the atom) and Tsallis-like (for the cavity) entropies. The impact of the initial state of the atom is also taken into account. The results shows that, in the first case, the $q$-parameter modifies appreciably the partial entropies, whereas in the second one, the way in which the inverse temperatures are distributed may led or not changes in the entropy functions.