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

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.

14 pages, 7 figures, two column

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• Bose-Einstein condensation and non-extensive statistics
• Non-Extensive Behaviour of the QCD Strong Coupling Constant
• Temperature fluctuations and Tsallis statistics in Relativistic Heavy Ion collisions
• Analytical Results for the Classical and Quantum Tsallis Hadron Transverse Momentum Spectra: the Zeroth Order Approximation and beyond
• QCD phase transition at finite temperature and chemical potential with the non-extensive statistics
• A harmonic oscillator in nonadditive statistics and a novel transverse momentum spectrum in high-energy collisions
• A possible correction of the Saha curve for non-equilibrium states
• Effective chemical potential and its phenomenological implications for the Hubble parameter
• Constraining Tsallis Corrections to Photon Reheating from Electron-Positron Annihilation: A Phenomenological Approach