Exact and approximate results of non-extensive quantum statistics

TL;DR

This paper introduces an analytical method to derive thermodynamical quantities in non-extensive quantum systems, comparing approximate and exact results for Bose-Einstein condensation and blackbody radiation.

Contribution

It develops an explicit analytical technique for non-extensive quantum statistics and compares approximate schemes with exact results, demonstrating their accuracy and simplicity.

Findings

Approximate methods closely match exact results up to first order in (q-1).

The factorization approach provides a simple and effective way to handle non-extensive quantum systems.

Results are consistent for Bose-Einstein condensation and blackbody radiation phenomena.

Abstract

We develop an analytical technique to derive explicit forms of thermodynamical quantities within the asymptotic approach to non-extensive quantum distribution functions. Using it, we find an expression for the number of particles in a boson system which we compare with other approximate scheme (i.e. factorization approach), and with the recently obtained exact result. To do this, we investigate the predictions on Bose-Einstein condensation and the blackbody radiation. We find that both approximation techniques give results similar to (up to ${\cal O}(q-1)$) the exact ones, making them a useful tool for computations. Because of the simplicity of the factorization approach formulae, it appears that this is the easiest way to handle with physical systems which might exhibit slight deviations from extensivity.