Scaled Bregman divergences in a Tsallis scenario

There exist two different versions of the Kullback–Leibler divergence (K–Ld) in Tsallis statistics, namely the usual generalized K–Ld and the generalized Bregman K–Ld. Problems have been encountered in trying to reconcile them. A condition for consistency between these two generalized K–Ld forms is derived by recourse to the additive duality of Tsallis statistics. It is also shown that the usual generalized K–Ld subjected to this additive duality, known as the dual generalized K–Ld, is a scaled Bregman divergence. This leads to an interesting conclusion: the dual generalized mutual information is a scaled Bregman information. The utility and implications of these results are discussed.