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.
Highlights
In the context of high-energy collisions, the observables in certain situations could be quantitatively explained better in terms of non-extensive statistics producing powerlaw distributions
We proceed to analyze the quantitative impact of non-extensivity in small (q − 1) limit along with the quantum corrections in terms of BE/FD statistics on various thermodynamic quantities, compared with the same under a Boltzmann generalization
The relativistic kinetic theory and the thermodynamic properties have been obtained in detail by generalizing the Bose–Einstein and Fermi–Dirac distributions in an non-extensive environment following the prescription introduced by Tsallis
Summary
In the context of high-energy collisions, the observables (such as particle spectra and transverse momentum fluctuations) in certain situations could be quantitatively explained better in terms of non-extensive statistics producing powerlaw distributions. The requirement of a generalized statistics, leading to a power-law kind of distribution of emitted particles in high-energy collisions, has been extensively studied [13,14,15,16,17,18,19,20]. This could be a hint towards the presence of longrange correlations among the particles within the system. The two-particle, long-range correlations in the systems created in collider experiments already have been identified in recent work where the correlation is quantified by the “ridge structure”, observed in particle multiplic-
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