A note on the thermodynamics of self-gravitating systems and its related astrophysics

Our previous works have shown the statistical mechanics of self-gravitating system. In this paper, we will first further analyse the physics behind it and propose that our statistical mechanics can be based on local ergodicity and Boltzmann entropy. With the method of statistical mechanics, we will show our definition of temperature and then the capacity of self-gravitating systems. Then we will preliminarily show the thermal stability of the thermodynamical equilibrium state in our theory. Our results also provide new explanations for observations and numerical simulations of dissipationless collapse, including that the gravothermal catastrophe may be only a special case of our results, and the non-universal density distribution in the simulations of dissipationless collapse may be not caused by a different initial collapse factor.