A new form of Tsallis distribution based on the probabilistically independent postulate

Abstract

The current form of Tsallis distribution for a Hamiltonian system with an arbitrary potential is found to represent a simple isothermal situation. In this letter, the q-exponential of a sum can be applied as the product of the q-exponential based on the probabilistically independent postulate employed in nonextensive statistical mechanics. Under this framework, a new form of Tsallis distribution is suggested. It is shown that the new form of Tsallis distribution can supply the statistical description for the nonequilibrium dynamical property of the Hamiltonian system governed by an arbitrary potential, and it is found to be one potential statistical distribution for the dark matter.

Non-extensive statistics and understanding particle production and kinetic freeze-out process from pT-spectra at 2.76 TeV

“…In a very recent study, the present author had taken up such an effort in dealing with pion-and kaon-spectra produced in P +P and P b+P b collisions at √ s N N = 2.76 TeV [1]. The main theoretical basis of the analysis was Tsallis non-extensive statistics which has, so far, been proven to be very useful in interpreting various aspects of high energy nuclear interactions by different theoretical as well as experimental groups [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,…”

Non-extensive statistics and a systematic study of meson-spectra at LHC energy $\sqrt{s_{NN}} = 2.76$ TeV

“…The analyses of particle-spectra with a suitable model/approach, thus, pave the way to get insights of the thermodynamical evolution of such a deconfined medium and it's cooling off through the process of hadronization. Analysis of such a system is statistical in nature; and Tsallis generalized non-extensive statistics, instead of usual Boltzmann-Gibbs statistics, has been proven, over the years, to be a good choice to deal with such a system [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39]. The mechanism behind the emergence of Tsallis-like spectra from such a hot and dense partonic matter, produced immediate after the nuclear interactions at ultrarelativistic energies, is yet to be understood theoretically.…”

The entropy in finite N-unit nonextensive systems: The normal average and q-average

“…Some related issues of the degree of freedom N on the PDF have been discussed in Refs. [26][27][28]. The nonextensivity-induced correlation has been calculated for classical ideal gas [29][30][31] and harmonic oscillator [30].…”