Relationships Between the Legendre Structure in the S2-q-Formalism and the Dually-Flat Structure in the Space of Escort Distributions

We explore the relationships between the Legendre structure in the S2-q-formalism in nonextensive statistical mechanics and the dually-flat structure in information geometry. The q-generalized thermodynamic potentials in the S2q-formalism are related to the dual potential functions in the information geometry.