Non-distributive algebraic structures derived from nonextensive statistical mechanics

TL;DR

This paper introduces a new multi-parametric non-distributive algebraic structure based on generalized logarithm and exponential functions, extending the mathematical framework of nonextensive statistical mechanics.

Contribution

It develops a novel multi-parametric algebraic structure derived from generalized functions, broadening the mathematical tools in nonextensive statistical mechanics.

Findings

Defines a two-parametric non-distributive algebraic structure.

Generalizes to multi-parametric structures with consistent limits.

Connects algebraic structures to nonextensive statistical mechanics.

Abstract

We propose a two-parametric non-distributive algebraic structure that follows from $(q,q')$-logarithm and $(q,q')$-exponential functions. Properties of generalized $(q,q')$-operators are analyzed. We also generalize the proposal into a multi-parametric structure (generalization of logarithm and exponential functions and the corresponding algebraic operators). All $n$-parameter expressions recover $(n-1)$-generalization when the corresponding $q_n\to1$. Nonextensive statistical mechanics has been the source of successive generalizations of entropic forms and mathematical structures, in which this work is a consequence.