$\kappa$-entropic statistical paradigm for relativistic corrections to the Heisenberg principle

Quantum Physics [Submitted on 15 Apr 2026] κ-entropic statistical paradigm for relativistic corrections to the Heisenberg principle Giuseppe Gaetano Luciano, Jaume Gin\' e, Daniel Chemisana The Heisenberg position-momentum uncertainty relation is a cornerstone of quantum mechanics. However, its standard formulation is not fully consistent with special relativity. While partial understanding has been achieved in the ultra-relativistic regime, a comprehensive description is still lacking, particularly in the intermediate velocity domain, where particle speeds remain well below the speed of light yet relativistic corrections are expected to become appreciable. This regime constitutes the most promising arena for experimentally probing relativistic modifications of quantum uncertainty. By adopting a variational approach, in this work we derive a relativistic extension of the Heisenberg algebra within the framework of \kappa-deformed Kaniadakis statistics. The latter emerges from the application of the Maximum Entropy Principle to Kaniadakis entropy, a one-parameter generalization of the Boltzmann-Gibbs-Shannon entropy naturally induced by Lorentz transformations. We investigate the physical implications of the resulting uncertainty relation, deriving constraints on the Kaniadakis parameter from precision measurements of the fine-structure constant and confronting our construction with other extensions discussed in the recent literature. Comments: 12 pages, 2 figures. We would greatly appreciate any comments or feedback Subjects: Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th) Cite as: arXiv:2604.13697 [quant-ph]   (or arXiv:2604.13697v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.13697 Focus to learn more Submission history From: Giuseppe Gaetano Luciano Dr [view email] [v1] Wed, 15 Apr 2026 10:24:31 UTC (59 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: hep-th References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)