  In this article, we investigate the thermodynamic stability of the FRW
universe for two examples, Tsallis entropy and loop quantum gravity, by
considering non-extensive statistical mechanics. The heat capacity, free energy
and pressure of the universe are obtained. For the Tsallis entropy model, we
obtained the constraint for $\beta$, namely, $1/2 < \beta < 2$. The free energy
of a thermal equilibrium universe must be less than zero. We suggest that the
reason for the accelerated expansion of the universe is not due to Tsallis
entropy. Similar results are obtained for loop quantum gravity. However, since
the values of $\Lambda(\gamma)$ and $q$ cannot be determined in this model, the
results become more subtle than that in the Tsallis entropy model. In addition,
we compare the results for the universe with those for a Schwarzschild black
hole.
