On the application of nonextensive statistical mechanics to the black-body radiation

Some results for the black-body radiation obtained in the context of the nonextensive statistical mechanics (normalized approach) are analyzed. Since the obtained elsewhere thermodynamic potential can be expressed in terms of Wrightʹs special function a useful asymptotic expansion can be obtained. This expansion allows to consider in a simple way the thermodynamic properties of the black-body radiation away from the Boltzmann–Gibbs limit q→1. The proposed approximation scheme is physically reasonable for the analysis of the cosmic background radiation. It is shown that while the internal energy remains extensive the application of the concepts of the nonextensive lead to the Td+1 Stefan–Boltzmann behavior.