The thermodynamic stability criterion in a self-gravitational system with phase transition

Abstract

In this paper, we analyze the heat capacity in a self-gravitational system, where there are two phases, in the framework of nonextensive statistical mechanics. We define one value which is the ratio of gas mass to total mass of the system. When the mass ratio is less than a critical value, the heat capacity of the system is positive, so the system is stable. If it is higher than this critical value, the system will be unstable. Then the thermodynamic instability, coupled with the gravitational instability, stimulates the evolution of the system. The liquefaction of the gas in the system, due to the high pressure and temperature inside it, leads to the decrease of gas mass ratio. This will continue until the system becomes stable. Therefore, one can find that phase transition plays an important role in maintaining the stability of such system.