Generalized algebra within a nonextensive statistics

Preprint

6 June 2003

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math-ph/0303061

Abstract

By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators : addition, subtraction, product and division, are generalized. The properties of the generalized operators are investigated. Some standard properties are preserved, e.g., associativity, commutativity and existence of neutral elements. On the contrary, the distributivity law and the opposite element is no more universal within the generalized algebra.

Keywords

NONEXTENSIVE STATISTICS
GENERALIZED LOGARITHM
GENERALIZED ALGEBRA
OPPOSITE ELEMENT
NEUTRAL ELEMENTS
COMMUTATIVITY
STATISTICS
PROPERTIES

All Related Versions

Version 1, 2003-03-26, ArXiv
Version 2, 2003-03-28, ArXiv
Version 3, 2003-04-03, ArXiv
Version 4, 2003-06-06, ArXiv
Published version: Reports on Mathematical Physics, 52 (3), 437.

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