The black-body radiation in Tsallis statistics

TL;DR

This paper explores black-body radiation within Tsallis non-extensive statistics, analyzing thermodynamic and statistical properties, especially deviations from classical laws like Stefan-Boltzmann, using special functions and approximation methods.

Contribution

It provides a detailed analysis of black-body radiation in Tsallis statistics, including asymptotic expansions and the impact of non-extensivity on radiation laws.

Findings

Asymptotic expansion of thermodynamic potentials using Wright's function

Deviations from T^4 Stefan-Boltzmann law for q<1

Discussion of approximation schemes for cosmic radiation

Abstract

Some results for the black-body radiation obtained in the context of the $q$-thermostatistics are analyzed on both thermodynamical and statistical-mechanical levels. Since the thermodynamic potentials can be expressed in terms of the Wright's special function an useful asymptotic expansion can be obtained. This allows the consideration of the problem away from the Boltzmann-Gibbs limit $q=1$. The role of non-extensivity, $q<1$, on the possible deviation from the Stefan-Boltzmann $T^{4}$ behavior is considered. The application of some approximation schemes widely used in the literature to analyze the cosmic radiation is discussed.