  The particle production in relativistic heavy-ion collisions seems to be
created in a dynamically disordered system which can be best described by an
extended exponential entropy. In distinguishing between the applicability of
this and Boltzmann-Gibbs (BG) in generating various particle-ratios, generic
(non)extensive statistics (GNS) is introduced to the hadron resonance gas
model. Accordingly, the degree of (non)extensivity is determined by the
possible modifications in the phase space. Both BG extensivity and Tsallis
nonextensivity are included as very special cases defined by specific values of
the equivalence classes $(c, d)$. We found that the particle ratios at energies
ranging between $3.8$ and $2760~$GeV are best reproduced by nonextensive
statistics, where $c$ and $d$ range between $\sim0.9$ and $\sim1$. The present
work aims at illustrating that the proposed approach is well capable to
manifest the statistical nature of the system on interest. We don't aim at
highlighting deeper physical insights. In other words, while the resulting
nonextensivity is neither BG nor Tsallis, the freezeout parameters are found
very compatible with BG and accordingly with the well-known freezeout
phase-diagram, which is in an excellent agreement with recent lattice
calculations. We conclude that the particle production is nonextensive but
should not necessarily be accompanied by a radical change in the intensive or
extensive thermodynamic quantities, such as internal energy and temperature.
Only, the two critical exponents defining the equivalence classes $(c, d)$ are
the physical parameters characterizing the (non)extensivity.
