Algebra and calculus for Tsallis thermostatistics

TL;DR

This paper develops a mathematical framework involving generalized algebraic operations inspired by Tsallis thermostatistics, including fields, derivations, and integrations, which do not revert to classical forms as the deformation parameter approaches zero.

Contribution

It introduces novel algebraic structures and calculus operations tailored to Tsallis thermostatistics, expanding the mathematical tools available for non-extensive thermodynamics.

Findings

Constructed generalized addition and multiplication operations

Developed derivations and integrations in the Tsallis-inspired framework

Operations do not reduce to classical ones as deformation parameter approaches zero

Abstract

We construct generalized additions and multiplications, forming fields, and division algebras inspired by the Tsallis thermo-statistics. We also construct derivations and integrations in this spirit. These operations do not reduce to the naively expected ones, when the deformation parameter approaches zero.