Distributivity and deformation of the reals from Tsallis entropy

We propose a one-parameter family R-q 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 a one-parameter family of field isomorphisms tau(q) between R and R-q through which an absolute value on R-q is introduced. This turns out to be a quasisymmetric map, whose metric and measure-theoretical implications are pointed out. (C) 2011 Elsevier B.V. All rights reserved.