Signals of non-extensive statistical mechanics in high energy nuclear collisions

Abstract

Starting from the presence of non-ideal plasma effects due to strongly coupled plasma in the early stage of relativistic heavy-ion collisions, we investigate, from a phenomenological point of view, the relevance of non-conventional statistical mechanics effects on the rapidity spectra of net proton yield at AGS, SPS and RHIC. We show that the broad rapidity shape measured at RHIC can be very well reproduced in the framework of a non-linear relativistic Fokker-Planck equation which incorporates non-extensive statistics and anomalous diffusion.

Non-extensive equilibration in relativistic matter

“…The latter provides a treatment in which, -after some transformations and re-interpretations of the usual thermal quantities, like the temperature, -the usual * E-mail: tsbiro@mail.k i.hu procedures produce non-exponential particle spectra and other deviations from the predictions of the naive thermal models. While in studying spectra stemming from small systems, like + − or and collisions the most characteristic features are related to a restriction in the longitudinal phase space showing in properties of the rapidity distribution N/ and in the occurence of the negative binomial multiplicity distribution [1][2][3][4][5], the transverse momentum distributions rather show an enlarged and possibly more fractally filled phase space [6,7]. There are several speculations on possible causes for such deformations, measured in a summerized way by a parameter used in Tsallis' non-extensive [8][9][10][11][12] entropy formula, or Rényi's extensive one [13].…”

Transverse momentum and pseudorapidity distributions of final-state particles and spatial structure pictures of an interacting system in p-Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV

“…We hope to use only one distribution to describe uniformly the spectra, and only one temperature to describe the mean effect of the temperature fluctuations. The good candidate is the Tsallis statistics which is widely used in high energy collisions [20][21][22][23][24][25][26][27][28][29]. The Tsallis statistics can be used not only for the whole interacting system but also for the singular source.…”

“…This renders a two-or multi-temperature emission picture which is in fact to fall into the framework of a multisource thermal model [17][18][19]. This also means that the interacting system has temperature changes (fluctuations) from a temperature to another one, which can be described by the Tsallis statistics [20][21][22][23][24][25][26][27][28][29].…”

“…In this paper, in the framework of the multisource thermal model [17][18][19], we use the Tsallis statistics [20][21][22][23][24][25][26][27][28][29] to describe the transverse momentum distributions of final-state particles produced in p-Pb collisions with different centrality intervals at √ s N N = 5.02…”

Nonextensive perfect hydrodynamics — a model of dissipative relativistic hydrodynamics?

“…The only works discussing some general features of the nonextensive hydrodynamics, which we are aware of [19][20][21], use a nonrelativistic approach and are therefore not suitable for the applications we are interested in. On the other hand it is known that an approach based on non-extensive statistical mechanics (used mainly in the form proposed by Tsallis [22][23][24][25][26][27][28] with only one new parameter, the nonextensivity parameter ) describes different sets of data in a better way than the usual statistical models based on BG statistics, cf., [22][23][24][25][26][27][28] for general examples and [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] for applications to multi-particle production processes. Roughly speaking, all observed effects amount to a broadening of the respective spectra of the observed secondaries (both in transverse momentum space and in rapidity space), they take the form of -exponents instead of the naively expected usual exponents: exp(−X /T ) =⇒ exp (−X /T ) = [1 − (1 − )X /T ] 1/ (1− ) .…”