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The hadron-resonance gas (HRG) model with the mass-proportional eigenvolume(EV) corrections is employed to fit the hadron yield data of the NA49collaboration 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 STARcollaboration for Au+Au collisions at $\sqrt{s_{\rm NN}} = 200$ GeV, and thehadron midrapidity yield data of the ALICE collaboration for Pb+Pb collisionsat $\sqrt{s_{\rm NN}} = 2760$ GeV. At given bombarding energy, for a given setof radii, the EV HRG model fits do not just yield a single $T-\mu_B$ pair, buta whole range of $T-\mu_B$ pairs, each with similarly good fit quality. Thesepairs form a valley in the $T-\mu_B$ plane along a line of nearly constantentropy per baryon, $S/A$, which increases nearly linearly with bombardingenergy $E_{\rm lab}$. The entropy per baryon values extracted from the data atthe different energies are a robust observable: it is almost independent of thedetails of the modeling of the eigenvolume interactions and of the specific$T-\mu_B$ values obtained. These results show that the extraction of thechemical freeze-out temperature and chemical potential is extremely sensitiveto the modeling of the short-range repulsion between the hadrons. This impliesthat the ideal point-particle HRG values are not unique. The wide range of theextracted $T$ and $\mu_B$ values suggested by the eigenvolume HRG fits, as wellas the approximately constant $S/A$ at freeze-out, are consistent with anon-equilibrium scenario of continuous freeze-out, where hadrons can bechemically frozen-out throughout the extended space-time regions during theevolution of the system. Even when the EV HRG fits are restricted to modesttemperatures suggested by lattice QCD, the strong systematic effects of EVinteractions are observed.

Examination of the sensitivity of the thermal fits to heavy-ion hadron yield data to the modeling of the eigenvolume interactions