https://doi.org/10.1140/epjp/s13360-025-06126-1
Regular Article
Energy-time uncertainty relation from entropy measures
1
División de Ciencias e Ingenierías, Departamento de Física, Universidad de Guanajuato, Loma del Bosque 103, 37150, León, GTO, México
2
Unidad Académica de Física, Universidad Autónoma de Zacatecas, Calzada Solidaridad esquina con Paseo a la Bufa S/N, 98060, Zacatecas, ZAC, México
Received:
4
December
2024
Accepted:
13
February
2025
Published online:
25
February
2025
In a previous study, it was shown that the generalized uncertainty principle can be derived from non-extensive entropies, particularly those depending only on the probability, denoted as 
in the literature. This finding reveals an intriguing connection between non-extensive statistics and quantum gravity. In the present work, we extend our previous result and derive a generalized energy-time uncertainty relation based on a measure of non-extensive entropies. Consequently, the dispersion relation undergoes modifications consistent with those obtained in other approaches to quantum gravity. We interpret these modifications as evidence of the non-extensive behavior of spacetime fluctuations at scales close to the Planck scale. While these effects are significant in this regime, they become negligible in the classical one, i.e., at low energies where the spacetime is smooth. As a consequence of the non-extensive behavior exhibited by spacetime at very small scales, the black hole radiation temperature undergoes quantum-level corrections, increasing in the case of 
and decreasing for the case of 
. Moreover, the modified uncertainty relation derived here predicts a maximum uncertainty in energy, of the order of Planck energy, and a minimum time interval, of the order of the Planck time, offering new insights into the fundamental structure of spacetime in the quantum regime.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
