Perspective on Tsallis statistics for nuclear and particle physics

Abstract

This is a concise introduction to the topic of nonextensive Tsallis statistics meant especially for those interested in its relation to high-energy proton–proton, proton–nucleus and nucleus–nucleus collisions. The three types of Tsallis statistics are reviewed. Only one of them is consistent with the fundamental hypothesis of equilibrium statistical mechanics. The single-particle distributions associated with it, namely Boltzmann, Fermi–Dirac and Bose–Einstein, are derived. These are not equilibrium solutions to the conventional Boltzmann transport equation which must be modified in a rather nonintuitive manner for them to be so. Nevertheless, the Boltzmann limit of the Tsallis distribution is extremely efficient in representing a wide variety of single-particle distributions in high-energy proton–proton, proton–nucleus and nucleus–nucleus collisions with only three parameters, one of them being the so-called nonextensitivity parameter [Formula: see text]. This distribution interpolates between an exponential at low transverse energy, reflecting thermal equilibrium, to a power law at high transverse energy, reflecting the asymptotic freedom of Quantum Chromodynamics (QCD). It should not be viewed as a fundamental new parameter representing nonextensive behavior in these collisions.