Distributivity and deformation of the reals from Tsallis entropy

Abstract

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.

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

References in corpus (1)

• A possible deformed algebra and calculus inspired in nonextensive thermostatistics

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