  The current status of implementing Tsallis (nonextensive) statistics on
high-energy physics is briefly reviewed. The remarkably low
freezeout-temperature, which apparently fails to reproduce the first-principle
lattice QCD thermodynamics and the measured particle ratios, etc. is discussed.
The present work suggests a novel interpretation for the so-called {\it
"Tsallis-temperature"}. It is proposed that the low Tsallis-temperature is due
to incomplete implementation of Tsallis algebra though exponential and
logarithmic functions to the high-energy particle-production. Substituting
Tsallis algebra into grand-canonical partition-function of the hadron resonance
gas model seems not assuring full incorporation of nonextensivity or
correlations in that model. The statistics describing the phase-space volume,
the number of states and the possible changes in the elementary cells should be
rather modified due to interacting correlated subsystems, of which the
phase-space is consisting. Alternatively, two asymptotic properties, each is
associated with a scaling function, are utilized to classify a generalized
entropy for such a system with large ensemble (produced particles) and strong
correlations. Both scaling exponents define equivalence classes for all
interacting and noninteracting systems and unambiguously characterize any
statistical system in its thermodynamic limit. We conclude that the nature of
lattice QCD simulations is apparently extensive and accordingly the
Boltzmann-Gibbs statistics is fully fulfilled. Furthermore, we found that the
ratios of various particle yields at extreme high and extreme low energies of
RHIC-BES is likely nonextensive but not necessarily of Tsallis type.
