q-Thermostatistics and the black-body radiation problem

Abstract

We give an exact information-theory treatment of the n-dimensional black-body radiation process in a non-extensive scenario. We develop a q-generalization of the laws of (i) Stefan–Boltzmann, (ii) Planck, and (iii) Wien, and show that conventional, canonical results are obtained at temperatures above 1 K. Classical relationships between radiation, pressure, and internal energy are recovered (independently of the q value). Analyzing the particles’ density for q ≈ 1, we see that the non-extensive parameter q introduces a 9ctitious chemical potential. We apply our results to experimental data on the cosmic microwave background and reproduce it with acceptable accuracy for di:erent temperatures (each one associated to a particular q value).