Pedro G. S. Cardoso | Searcharxiv

arXiv2009

Some properties of deformed $q$-numbers

Nonextensive statistical mechanics has been a source of investigation in mathematical structures such as deformed algebraic structures. In this work, we present some consequences of $q$-operations on the construction of $q$-numbers for all numerical sets. Based on such a construction, we present a new product that distributes over the $q$-sum. Finally, we present different patterns of $q$-Pascal's triangles, based on $q$-sum, whose elements are $q$-numbers.

math-ph↗

arXiv2008

Non-distributive algebraic structures derived from nonextensive statistical mechanics

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.

cond-mat.stat-mech↗