  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.
