Tsallis' Statistics without probability distributions. REPLY to Comment on "Possible Divergences in Tsallis' Thermostatistics"

TL;DR

This paper defends a method to eliminate divergences in Tsallis' nonextensive statistical mechanics using a q-Laplace transform, clarifying previous criticisms and highlighting its advantages.

Contribution

It introduces a q-Laplace transformation approach to address divergences in Tsallis' statistics, providing a clearer understanding and defense of the original method.

Findings

Divergences in Tsallis' statistics can be mitigated with q-Laplace transform

The proposed method offers a consistent way to handle nonextensive systems

Clarifies misconceptions raised in previous commentaries

Abstract

In a recent letter (EPL, 104 (2013) 60003) we suggested a way to avoid divergences inherent to the formulation of nonextensive statistical mechanics. They can be eliminated via the use of a q-Laplace transformation, which was illustrated for the case of the harmonic oscillator. Lutsko and Boon now contend, in an interesting comment, that our new formulation raises questions that they carefully discuss. Here we elaborate an explanation of the contents of (EPL, 104 (2013) 60003) that permits to appreciate our original Letter in a more positive fashion.