A possible deformed algebra and calculus inspired in nonextensive thermostatistics

2003/04/30 by Ernesto P. Borges · 9 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Fractional Differential Equations Solutions #Statistical Mechanics and Entropy #cond-mat.stat-mech

paper · pdf · doi:10.1016/j.physa.2004.03.082

published as Physica A 340, 95--101 (2004) · 7 pages, no figures

openalex publication_date 2004/04/21 · arxiv created 2004/08/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a deformed algebra related to the q-exponential and the q-logarithm functions that emerge from nonextensive statistical mechanics. We also develop a q-derivative (and consistently a q-integral) for which the q-exponential is an eigenfunction. The q-derivative and the q-integral have a dual nature, that is also presented.

Cited by

• Mother wavelet functions generalized throughq-exponentials
• On Shore and Johnson properties for a Special Case of Csiszár f-divergences
• Generalized Algebra Grounded on Nonadditive Entropies
• Generalized Statistics Framework for Rate Distortion Theory with Bregman Divergences
• Deformed special relativity based on α-deformed binary operations
• Fractal Social Dynamics as a Driver of Consensus and Inequality
• Fisher metric from relative entropy group
• An Extended Model of Fractional-Dimensional Space for Anisotropic Solids with Deformed Derivatives
• Scaling property and the generalized entropy uniquely determined by a fundamental nonlinear differential equation

Related

• Deformed mathematical objects stemming from the q-logarithm function
• On the q-Laplace transform in the non-extensive statistical physics
• Deformed Heisenberg algebra: origin of q-calculus
• New exponential, logarithm and q-probability in the non-extensive statistical physics
• Semiclassical statistical mechanics' tools for deformed algebras