Quasi-power laws in multiparticle production processes

Abstract

We review the ubiquitous presence in multiparticle production processes of quasi-power law distributions (i.e., distributions following pure power laws for large values of the argument but remaining finite, usually exponential, for small values). Special emphasis is placed on the conjecture that this reflects the presence in the produced hadronic systems of some intrinsic fluctuations. If described by parameter q they form, together with the scale parameter T ("temperature"), basis of Tsallis distribution,, frequently used to describe the relevant distributions (the X being usually a transverse momentum). We discuss the origin of such quasi-power law behavior based on our experience with the description of multiparticle production processes. In particular, we discuss Tsallis distribution with complex nonextensivity parameter q and argue that it is needed to describe log-oscillations as apparently observed in recent data on large momentum distributions in very high energy p-p collisions.

Nonextensive Quasiparticle Description of QCD Matter

“…[8][9][10] and references therein). As a result, some quantities become non-extensive and develop power-law tailed rather than exponential distrubutions, making application of the usual BG statistics questionable (cf., [11,12] and references therein). The remedy is either to supplement the BG statistics by some additional dynamical input or, when it is not known, to use some form of nonextensive statistics generalizing the BG one, for example Tsallis statistics [13,14].…”

The emergence of self-organization in complex systems–Preface

“…Superstatistics was proposed to be a rigorous way to derive Tsallis statistics from a dynamical model [12]. The Tsallis dis-tribution is in fact the main topic of paper [21], where the authors discuss the ubiquitous presence of quasi-power law distributions in multiparticle production processes. In fact, the Tsallis distribution is essentially a inverse power-law function for large values and it was derived in the framework of a nonequilibrium statistical model involving the minimization of a non-extensive entropy (see discussion and references in paper [21]).…”

“…The Tsallis dis-tribution is in fact the main topic of paper [21], where the authors discuss the ubiquitous presence of quasi-power law distributions in multiparticle production processes. In fact, the Tsallis distribution is essentially a inverse power-law function for large values and it was derived in the framework of a nonequilibrium statistical model involving the minimization of a non-extensive entropy (see discussion and references in paper [21]). The Tsallis entropy and distribution represent an attempt to build a non-standard statistical mechanics for complex systems, and superstatistics proved to be compatible with systems whose complexity originates from non-homogeneity of some physical parameter in the medium supporting the anomalous transport.…”

“…Papers [18,19,20,21,22,23] are mainly devoted to anomalous transport in complex media and complex materials, from complex fluids to porous media. In these systems complexity is intimately connected with some physical properties that are heterogeneously distributed, even if, in some applications, the medium can be considered statistically homogeneous (see paper [20]).…”

An example of the interplay of nonextensivity and dynamics in the description of QCD matter

“…[1][2][3][4][5] and references therein for details). Such an environment can be described by a nonextensive statistics, which is usually taken to be in the form of Tsallis statistics [6][7][8] and is characterized by a parameter of nonextensivity, q = 1 (for q = 1 one recovers the usual Boltzmann-Gibbs statistics).…”