Temperature fluctuations and Tsallis statistics in Relativistic Heavy Ion collisions

Abstract

We study temperature fluctuations in the initial stages of the relativistic heavy ion collision. We obtain the spectrum of the temperature fluctuations for the peripheral collisions, assuming that the fluid is turbulent. We find that the length scale of the temperature fluctuation is of the order of 1.16 fm. We find that while temperature fluctuations in the initial time steps can be fitted with a Gaussian distribution, temperature fluctuations in the later stages can be better fitted with the q-Gaussian distribution. This distribution is associated with the Tsallis statistics. We use the Tsallis statistics to study the turbulence in the relativistic heavy ion collisions. We obtain the value of the entropic index from the temperature spectrum. A detailed analysis of the dependence of the entropic index on the system parameters is done. We compare our results with recent experimental results and find the general results of the experimental data are in agreement with our results. Our work indicates that the turbulent motion of the relativistic heavy ion fluid should be studied by using a non-extensive formalism.

Centrality, transverse momentum and collision energy dependence of the Tsallis parameters in relativistic heavy-ion collisions

“…A non-extensive Tsallis statistics [1,2] has been shown to provide a better description of the nature of the non-exponential transverse momentum spectrum. The description of particle spectra using the Tsallis distribution has gained lots of interest recently because these could successfully explain the underlying physics in proton-proton (pp), proton-nucleus (p−A), and nucleus-nucleus (A−A) collision systems in dedicated facilities at the Relativistic Heavy-Ion collider (RHIC) and the Large Hadron Collider (LHC) [3][4][5][6][7][8][9][10][11][12]. Transverse momentum spectra of identified hadrons have significant importance to understand the collision dynamics, particle production mechanism, and thermodynamic behavior of the system.…”