  We have studied the classical and quantum expressions of electrical
conductivity and their numerical estimation in the presence of a magnetic field
for hadron resonance gas (HRG) and massless quark matter. Classical results of
transport coefficients of HRG matter in the presence of a magnetic field were
studied previously by Dash et al. [Phys. Rev. D 102, 016016 (2020)] using the
standard relaxation time approximation in the Boltzmann equation. In the same
reference, the transition from isotropic transport coefficients to anisotropic
coefficients in the presence of a magnetic field was also estimated for
massless and HRG matter. This led to an upper limit or Stefan-Boltzmann (SB)
type limit to the nonperturbative domain transition of transport coefficients.
In a similar context, the present work has concentrated on the classical to
quantum transition of HRG transport from the domain of high temperature and low
magnetic field to that of low temperature and high magnetic field. We have also
compared the quantum modification of HRG results with that of massless quark
matter, where we observed an opposite trend. A similar kind of quantum effect
is also noticed between mesons and baryons due to their different particle
distribution functions. Despite the fact that HRG contains both mesons and
baryons, Landau quantization of its net magnetothermodynamic phase space
reveals meson- or boson-dominated quantum modification. That is why the quantum
modification of HRG results reveals the opposite trend from that of massless
quark matter, which faces fermionic quantum modification.
