Thermodynamics and relativistic kinetic theory for q-generalized Bose–Einstein and Fermi–Dirac systems

Abstract

The thermodynamics and covariant kinetic theory are elaborately investigated in a non-extensive environment considering the non-extensive generalization of BoseEinstein (BE) and Fermi-Dirac (FD) statistics. Starting with Tsallis' entropy formula, the fundamental principles of thermostatistics are established for a grand canonical system having q-generalized BE/FD degrees of freedom. Many particle kinetic theory is set up in terms of the relativistic transport equation with q-generalized Uehling-Uhlenbeck collision term. The conservation laws are realized in terms of appropriate moments of the transport equation. The thermodynamic quantities are obtained in a weak non-extensive environment for a massive pion-nucleon and a massless quark-gluon system with non-zero baryon chemical potential. In order to get an estimate of the impact of non-extensivity on the system dynamics, the q-modified Debye mass and hence the qmodified effective coupling are estimated for a quark-gluon system.

Bose-Einstein condensation and non-extensive statistics

“…The non-extensive thermodynamics of quantum systems has been studied in [13,14]. It has been applied to investigate some systems, specially hadronic systems [26], with large implications in the study of, e.g., can be hadrons, quark-gluon plasma and neutronstars.…”

“…While BEC has been exhaustively studied under the light of the BG Statistics [10][11][12], the same does not hold for the Tsallis Statistics. Apart from a few works on the S q for quantum systems [13][14][15][16][17], and some applications for BEC, there is a lack of information on the behaviour of the condensates following the non-additive entropy. In this work we provide a detailed description of the non-extensive BEC, or qBEC.…”

Analytical Results for the Classical and Quantum Tsallis Hadron Transverse Momentum Spectra: the Zeroth Order Approximation and beyond

“…However, it has been explicitly verified that the residues at those poles have drastically diminishing contributions, and for all the practical purposes, considering only a few terms of Eqs. (26), and (38) suffices.…”

Solid/Liquid Phase Transition and Heat Engine in Asymptotically Flat Schwarzschild Black Hole via the Rényi Extended Phase Space Approach

“…To address these isssues, we may need to use an alternative choice of the generalized entropy function. Recently, the Tsallis [9] and Rényi [10] entropies, which is based on the power law probability distribution, has been used to study strongly interacting phenomena in particle physics [11][12][13], kinetic theory [14][15][16] and complex systems [17]. A comprehensive description of generalized entropies and its applications has been found in [18].…”