Thermodynamics of the Bose gas and black radiation in non-extensive Tsallis statistics

The aim of this work is to construct the thermodynamics of open quantum nonextensive systems of elementary Bose-gas particles in the framework of Tsallis statistics based on modified quantum entropy, which depends on the real number $q$. Generalized expressions for the thermodynamic potential, internal energy, free energy, specific heat and pressure, as well as the basic thermodynamic equations are obtained. Modified equilibrium Bose–Einstein distributions for bulk particles and generalized Planck, Rayleigh–Jeans, and Wien laws for photons that can be applied to various physical problems, in particular, to the description of black cosmic radiation, are discussed. The initial basis for such a consideration is the assumption that the distribution of photons of cosmic background radiation (in thermal equilibrium) may differ from the classical Planck distribution due to the influence of long-range gravitational effects at large distances. This influence is probably a reflection of the fact remote in time, according to which matter and light were strongly interconnected.
The generalized thermodynamics of photon gas can be used, in particular, as a theoretical justification for experimental studies of ink radiation inside various astrophysical objects.