Distributivity and deformation of the reals from Tsallis entropy

Details Distributivity and deformation of the reals from Tsallis entropy Distributivity and deformation of the reals from Tsallis entropy

2011-04-13

arxiv.org/abs/1104.2396v2

Physica A 391, (2012) 1120-1127

Physics

Mathematical Physics

16 pages, Standard LaTeX2e, To be published in Physica A

Scientific paper

We propose a one-parameter family \ $\mathbb{R}_q$ \ 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 \ $\mathbb{R}$ \ and \ $\mathbb{R}_q$ \ through which an absolute value on \ $\mathbb{R}_q$ \ is introduced. This turns out to be a quasisymmetric map, whose metric and measure-theoretical implications are pointed out.

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