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

Abstract

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 nonex-tensive entropic scheme can be consistent with the space-time ideas contained in the general rela-tivistic theory. The constructed kinetic equation is designed to describe a wide range of phenomena in as-trophysics, cosmology and high-energy physics, in particular, multiparticle production processes in relativistic collisions.