In the present paper we introduce generalized kinetic equations describing the dynamics of a system of interacting gas and photons obeying to a very general statistics. In the space homogeneous case we study the equilibrium state of the system and investigate its stability by means of Lyapounov's theory. Two physically relevant situations are discussed in details: photons in a background gas and atoms in a background radiation. After having dropped the statistics generalization for atoms but keeping the statistics generalization for photons, in the zero order Chapmann-Enskog approximation, we present two numerical simulations where the system, initially at equilibrium, is perturbed by an external isotropic Dirac's delta and by a constant source of photons. Recently,in [14], a generalized kinetic theory has been proposed by Rossani and Kaniadakis, with the purpose to deal, at a kinetic level, particles obeying to a generalized statistics. Following this idea, generalized kinetic theories of electrons and photons [15] as well as electrons and phonons [16] have been proposed. In this paper we present, as a natural continuation of the previous works, a kinetic theory of interacting atoms and photons obeying to a very general statistics. We recall that in the last years a classical kinetic approach in the study of this dynamical problem has been proposed for the case of two energy levels [17,18] and further generalized for multi-levels atoms and multi-frequencies photons [19,20]. The most remarkable feature is that this approach allows a self-consistent derivation, at equilibrium, of Planck's law. The physical system we deal with is constituted by atoms A ℓ (ℓ = 1, 2, · · · , N) with mass m, endowed with a finite number n of internal energy levels 0 = E 1 < E 2 < · · · < E n , with transitions from one state to another made possible by either scattering between particles, or by their interaction with a self-consistent radiation field made up by photons p ij with intensity I ij , i < j = 1, 2, · · · , n, at the n (n − 1)/2 frequencies ω ij = E j − E i (we adopt natural unitsh = c = 1). According to the relevant literature [21], we assume that the following interactions take place: a) elastic and inelastic interactions between particles, b) emission and absorption of photons. We restrict ourselves to the most common and physical interaction mechanism between particles:where i ≤ j. The most general reaction [19] does not introduce significant improvement with respect to the present simplification. Gas-radiation interaction processes include:
