  The thermodynamic stability conditions (TSC) of nonadditive and composable
entropies are discussed. Generally the concavity of a nonadditive entropy with
respect to internal energy is not necessarily equivalent to the corresponding
TSC. It is shown that both the TSC of Tsallis' entropy and that of the
$\kappa$-generalized Boltzmann entropy are equivalent to the positivity of the
standard heat capacity.
