Comments on "Superstatistical properties of the one-dimensional Dirac oscillator" by Abdelmalek Boumali et al

TL;DR

This comment critiques Boumali et al.'s superstatistical analysis of the 1D Dirac oscillator, emphasizing the importance of correct partition function calculation and the preservation of thermodynamic structure for accurate results.

Contribution

It clarifies the proper mathematical formalism and partition function considerations necessary for accurate superstatistical thermodynamics of the Dirac oscillator.

Findings

Incorrect partition function led to divergences in free energy

Proper inclusion of all poles removes divergences

Restrictions on the q-parameter are unnecessary with correct partition function

Abstract

In this comment, we discuss the mathematical formalism used in Boumali et al. (2020) which describes the superstatistical thermal properties of a one-dimensional Dirac oscillator. In particular, we point out the importance of maintaining the Legendre structure unaltered to ensure an accurate description of the thermodynamic observables when a Tsallis-like statistical description is assumed. Also, we remark that all the negative poles have to take into account to calculate the Gibbs--Boltzmann partition function. Our findings show that the divergences obtained by the authors in the Helmholtz free energy, which are propagated to the other thermal properties, are a consequence of an incomplete partition function. Moreover, we prove that the restrictions over the $q$-parameter are no needed if an appropriate partition function describes the system.