Towards a derivation, within the framework of Tsallis statistics relativistic kinetic equation for a rarefied ideal gas system of high-energy particles

In this work we discuss the nonextensive kinetic theory for anomalous gas $q$-systems in a general relativistic framework. By including nonextensive effects in the collision term of the relativistic equation (violating Boltzmann molecular chaos hypothesis) and in a modified $4$-vector expression for the $q$-entropy flux it is shown that the entropic Tsallis formalism preserves a local form of the relativistic $H$-theorem according to which the entropy growth in any point of space-time is never negative. It is shown that the local collision equilibrium (the zero-point entropy source term) is described by a generalized version of the Yuttner relativistic distribution. Using this distribution, the particle number, energy and entropy densities and the thermal equation of state for a relativistic $q$-gas of identical particles in the equilibrium state are determined explicitly. The results are reduced to the standard ones in the extensive limit, thus showing that the nonextensive entropic scheme can be consistent with the space-time ideas contained in the general relativistic theory.
The constructed kinetic equation is designed to describe a wide range of phenomena in astrophysics, cosmology and high-energy physics, in particular, multiparticle production processes in relativistic collisions.