Systematic Analysis of the Non-extensive Statistical Approach in High Energy Particle Collisions - Experiment vs. Theory

The analysis of high-energy particle collisions is an excellent testbed for the non-extensive statistical approach. In these reactions we are far from the thermodynamical limit. In small colliding systems, such as electron-positron or nuclear collisions, the number of particles is several orders of magnitude smaller than the Avogadro number; therefore, finite-size and fluctuation effects strongly influence the final-state one-particle energy distributions. Due to the simple characterization, the description of the identified hadron spectra with the Boltzmann-Gibbs thermodynamical approach is insufficient. These spectra can be described very well with Tsallis-Pareto distributions instead, derived from non-extensive thermodynamics. Using the $q$-entropy formula, we interpret the microscopic physics in terms of the Tsallis $q$ and $T$ parameters. In this paper we give a view on these parameters, analyzing identified hadron spectra from recent years in a wide center-of-mass energy range. We demonstrate that the fitted Tsallis-parameters show dependency on the center-of-mass energy and particle species (mass). Our findings are described well by a QCD (Quantum Chromodynamics) inspired parton evolution ansatz. Based on this comprehensive study, apart from the evolution, both mesonic and baryonic components found to be non-extensive ($q>1$), besides the mass ordered hierarchy observed in the parameter $T$. We also study and compare in details the theory-obtained parameters for the case of PYTHIA8 Monte Carlo Generator, perturbative QCD and quark coalescence models.