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 q. 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.
Bibliographical noteFunding Information:
This work was supported by the U.S. Department of Energy Grant DE-FG02-87ER40328.
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- Statistical mechanics
- Tsallis distributions
- high energy nuclear and particle collisions