Negative heat capacity and non-extensive kinetic theory

The negative nature of the heat capacity $C_V$ of thermodynamically isolated self-gravitating systems is rediscussed in the framework of a non-extensive kinetic theory. It is found that the dependence of $C_V$ on the non-extensive parameter $q$ gives rise to a negative branch with the critical value corresponding to $q=5\mathrm{/}3$ ($C_V\to -\mathrm{\infty }$).