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

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.