A first order Tsallis theory

TL;DR

This paper develops a first-order approximation framework for Tsallis' entropy and its MaxEnt solutions, avoiding poles present in previous approaches and aligning with existing ozone layer data.

Contribution

It introduces a pole-free first-order approximation method for Tsallis entropy and its MaxEnt solutions, enhancing the theoretical understanding of non-extensive entropy.

Findings

Derived pole-free first-order solutions for Tsallis entropy

Demonstrated compatibility with ozone layer data

Provided a more stable approximation framework for Tsallis' approach

Abstract

We investigate first-order approximations to both i) Tsallis' entropy $S_q$ and ii) the $S_q$-MaxEnt solution (called q-exponential functions $e_q$). It is shown that the functions arising from the procedure ii) are the MaxEnt solutions to the entropy emerging from i). The present treatment is free of the poles that, for classic quadratic Hamiltonians, appear in Tsallis' approach, as demonstrated in [Europhysics Letters {\bf 104}, (2013), 60003]. Additionally, we show that our treatment is compatible with extant date on the ozone layer.