  The hadron-resonance gas (HRG) model with the mass-proportional eigenvolume
(EV) corrections is employed to fit the hadron yield data of the NA49
collaboration for central Pb+Pb collisions at $\sqrt{s_{_{\rm NN}}} = 6.3, 7.6,
8.8, 12.3,$ and $17.3$ GeV, the hadron midrapidity yield data of the STAR
collaboration for Au+Au collisions at $\sqrt{s_{\rm NN}} = 200$ GeV, and the
hadron midrapidity yield data of the ALICE collaboration for Pb+Pb collisions
at $\sqrt{s_{\rm NN}} = 2760$ GeV. At given bombarding energy, for a given set
of radii, the EV HRG model fits do not just yield a single $T-\mu_B$ pair, but
a whole range of $T-\mu_B$ pairs, each with similarly good fit quality. These
pairs form a valley in the $T-\mu_B$ plane along a line of nearly constant
entropy per baryon, $S/A$, which increases nearly linearly with bombarding
energy $E_{\rm lab}$. The entropy per baryon values extracted from the data at
the different energies are a robust observable: it is almost independent of the
details of the modeling of the eigenvolume interactions and of the specific
$T-\mu_B$ values obtained. These results show that the extraction of the
chemical freeze-out temperature and chemical potential is extremely sensitive
to the modeling of the short-range repulsion between the hadrons. This implies
that the ideal point-particle HRG values are not unique. The wide range of the
extracted $T$ and $\mu_B$ values suggested by the eigenvolume HRG fits, as well
as the approximately constant $S/A$ at freeze-out, are consistent with a
non-equilibrium scenario of continuous freeze-out, where hadrons can be
chemically frozen-out throughout the extended space-time regions during the
evolution of the system. Even when the EV HRG fits are restricted to modest
temperatures suggested by lattice QCD, the strong systematic effects of EV
interactions are observed.
