The imprints of superstatistics in multiparticle production processes

Abstract

Abstract:We provide an update of the overview of imprints of Tsallis nonextensive statistics seen in a multiparticle production processes. They reveal an ubiquitous presence of power law distributions of different variables characterized by the nonextensivity parameter > 1. In nuclear collisions one additionally observes adependence of the multiplicity fluctuations reflecting the finiteness of the hadronizing source. We present sum rules connecting parameters obtained from an analysis of different observables, which allows us to combine different kinds of fluctuations seen in the data and analyze an ensemble in which the energy (E), temperature (T) and multiplicity (N) can all fluctuate. This results in a generalization of the so called Lindhard's thermodynamic uncertainty relation. Finally, based on the example of nucleus-nucleus collisions (treated as a quasi-superposition of nucleon-nucleon collisions) we demonstrate that, for the standard Tsallis entropy with degree of nonextensivity < 1, the corresponding standard Tsallis distribution is described by = 2 − > 1.

Correlations from generalized thermodynamic uncertainty relations

“…In this presentation we shall not go into the details of Tsallis statistics and its applications in the field of multiparticle production observed in high energy experiments (see [2,9]). Here we concentrate on the problem of the coexistence and interconnection between fluctuations observed in different observables and, in particular, on the possible correlation between them which can, presumably, be measured experimentally.…”

“…Cf. [2] for further references concerning applications of this approach. Recent examples of spectacular power-like behavior has been reported by PHENIX [7] and CMS [8] recently.…”

“…Recent examples of spectacular power-like behavior has been reported by PHENIX [7] and CMS [8] recently. 2 Where…”

“…The proposition put forward some time ago is that, rather than invalidating a simple statistical approach, these observations call for its modification towards inclusion of a possible intrinsic, nonstatistical fluctuations, usually identified with fluctuations of the parameter T identified with the "temperature" of the hadronizing fireball (cf. reviews [2]). The introduced parameter q, known as the nonextensivity parameter, is shown to be directly connected to the variance of T ,…”

Tsallis Distribution Decorated with Log-Periodic Oscillation

“…As shown in [29] (cf., also, [22,23,[78][79][80]), the nonextensivity parameter q can be treated as a measure of the thermal bath heat capacity C with:…”