The stability of a non-extensive relativistic Fermi system

Based on the statistical theory of non-extensive relativity, and using theoretical analysis and numerical simulation, the non-extensive mechanical stability of ultra-relativistic free Fermi gas is investigated. The expressions of the stability conditions under high and low temperatures are given, and the mechanisms of the influences of temperature, ultra-relativistic effect, and non-extensive parameter q on stability are analysed. Our results show that at high temperature and under the condition of q<1, the stability of a non-extensive system is weaker than that of an extensive system, and the relativistic effect reduces system stability as compared with a non-relativistic system. However, under the condition of q>1, the stability of the non-extensive system is stronger than that of the extensive system, and the relativistic effect strengthens the system stability as compared with the non-relativistic system. In addition, under the condition of low temperature, the variation of the stability of the non-extensive system with temperature has a turning point.