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

TL;DR

This paper develops a non-extensive thermodynamic and kinetic framework for q-generalized Bose-Einstein and Fermi-Dirac systems, applying it to particle systems like pion-nucleon and quark-gluon, and analyzing the effects of non-extensivity.

Contribution

It introduces a covariant kinetic theory with q-generalized collision terms based on Tsallis' entropy, extending thermodynamics to non-extensive quantum systems.

Findings

Derived thermodynamic quantities for non-extensive systems.

Estimated q-modified Debye mass and effective coupling.

Analyzed impact of non-extensivity on system dynamics.

Abstract

The thermodynamics and covariant kinetic theory have been 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 have been established for a grand canonical system having q-generalized BE/FD degrees of freedom. The many particle kinetic theory has been set up in terms of the relativistic transport equation with q-generalized Uehling-Uhlenbeck collision term. The conservation laws have been realized in terms of appropriate moments of the transport equation. The thermodynamic quantities have been obtained in 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 have been estimated for a quark-gluon system.