  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.
