  Our previous works have shown the statistical mechanics of self-gravitating
system. In this paper, we will show its thermodynamics and compare our results
with observations and simulations. We propose that our statistical mechanics
can be based on ergodicity breaking and Boltzmann entropy, and its assumptions
do not contradict with the reality. With the principle of statistical
mechanics, we will show our definition of temperature and then the capacity of
self-gravitating systems. We find that the gravothermal catastrophe may be a
special case of our theory. Our results also provide new explanations for the
density profiles of observations and numerical simulations, especially we think
that the non-universal density distribution in the simulations of
dissipationless collapse is not caused by the different initial collapse
factor. We will also discuss about the core-cusp problem.
