  The pseudo-additive relation that the Tsallis entropy satisfies has nothing
whatsoever to do with the super- and sub- additivity properties of the entropy.
The latter properties, like concavity and convexity, are couched in geometric
inequalities and cannot be reduced to equalities. Rather, the pseudo-additivity
relation is a functional equation that determines the functional forms of the
random entropies. The Arimoto entropy satisfies a similar pseudo-additive
relation and yet it is a first order homogeneous form. Hence no conclusions can
be drawn on the extensive nature of the system from either the Tsallis or
Arimoto entropy based on the pseudo-additive equation.
