Generalizing the group structure of the Euclidean space, we construct a Riemannian metric on the deformed set Rqn induced by the Tsallis entropy composition property. We show that the Tsallis entropy is a “hyperbolic analogue” of the “Euclidean” Boltzmann/Gibbs/Shannon entropy and find...

We propose a one-parameter family Rq of deformations of the reals, which is motivated by the generalized additivity of the Tsallis entropy. We introduce a generalized multiplication which is distributive with respect to the generalized addition of the Tsallis entropy. These operations establish...