Nonextensive Statistical Mechanics and Nonlinear Dynamics

Introduction to Nonextensive Statistical Mechanics

“…A mechanical foundation of statistical mechanics from first principles should essentially include, in one way or another, the following main steps [40].…”

“…40 Time evolution of the temperature (calculated as twice the average kinetic energy per particle) for three single events representative of the three different classes observed at U = 0.69 for initial magnetization M 0 = 1. The size of the system is N = 20, 000 (from[46]).…”

Breather structures in degenerate relativistic non-extensive plasma

“…Since Tsallis (1988) proposed the generalization of the Boltzmann–Gibbs–Shanon (BGS) entropy, by adopting a thermo-statistical theory in a way that it becomes non-additive, a great deal of attention has been paid to the Tsallis statistics (Silva, Plastino & Lima 1998; Tsallis 2001; Gell-Mann & Tsallis 2004; Martinenko & Shivamoggi 2004; Dubinova & Dubinov 2006; Tribeche, Djebarni & Amour 2010; El-Awady & Moslem 2011; Alinejad & Shahmansouri 2012; El-Taibany & Tribeche 2012; Shahmansouri & Tribeche 2012; Akhtar, El-Taibany & Mahmood 2013; Bains, Li & Tribeche 2013; Shahmansouri & Tribeche 2013; Shahmansouri & Alinejad 2013 a , b ; Ashraf et al. 2014; El-Shamy, Tribeche & El-Taibany 2014; Ourabah & Tribeche 2014; Rahman & Ali 2014; Akhtar et al.…”

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.…”