Abstract
The transverse momentum distribution of identified hadrons from recent years are analyzed within the thermodynamically consistent formulation of non-extensive statistics. A wide range of center-of-mass energies and average event multiplicities are studied for various hadron species. We demonstrate that the average event multiplicity is a key variable in the study of high-energy collisions and a smooth transition in the description from small to large systems is possible. For this purpose the non-extensive statistical approach is more than appropriate. The validity of the non-extensive description is explored in multiple ways: such as the calculation of integrated yields per unit rapidity, the analysis of radial flow and the consistency check of the thermodynamical variables. The 'Tsallis-thermometer' is introduced as an indicator of quark-gluon plasma in small collisional systems.
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