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Our previous works have shown the statistical mechanics of self-gravitatingsystem. In this paper, we will show its thermodynamics and compare our resultswith observations and simulations. We propose that our statistical mechanicscan be based on ergodicity breaking and Boltzmann entropy, and its assumptionsdo not contradict with the reality. With the principle of statisticalmechanics, we will show our definition of temperature and then the capacity ofself-gravitating systems. We find that the gravothermal catastrophe may be aspecial case of our theory. Our results also provide new explanations for thedensity profiles of observations and numerical simulations, especially we thinkthat the non-universal density distribution in the simulations ofdissipationless collapse is not caused by the different initial collapsefactor. We will also discuss about the core-cusp problem.

Different thermodynamics of self-gravitating systems and discussions for some observations and simulations