Eur. Phys. J. C (2018) 78: 66
https://doi.org/10.1140/epjc/s10052-018-5536-3

Regular Article - Theoretical Physics

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

Indian Institute of Technology Gandhinagar, Palaj, Gandhinagar, Gujarat, 382355, India

^* e-mail: sukanyam@iitgn.ac.in

Received: 20 October 2017
Accepted: 9 January 2018
Published online: 24 January 2018

Abstract

The thermodynamics and covariant kinetic theory are elaborately investigated in a non-extensive environment considering the non-extensive generalization of Bose–Einstein (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 q-modified effective coupling are estimated for a quark–gluon system.