https://doi.org/10.1140/epjc/s10052-026-15348-1
Regular Article - Theoretical Physics
Thermodynamic stability and geometric thermodynamics of regular Bardeen AdS black hole using Kaniadakis statistics
Independent Researcher, Assam, India
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
27
November
2025
Accepted:
16
January
2026
Published online:
31
January
2026
Abstract
In this study, we investigate the thermodynamic stability and geometric thermodynamics of the regular Bardeen-AdS black hole within the framework of Kaniadakis statistics, incorporating the 
-deformed entropy. By varying both the Kaniadakis parameter and the black hole parameters, we uncover additional -dependent thermodynamic branches, singularities, and divergence points that are absent in the standard (
) case. The physical relevance of these new features is confirmed through geometric thermodynamics: curvature scalars computed from both the Quevedo geometrothermodynamic (GTD) and HPEM metrics precisely coincide with the phase transition points and divergence points identified from heat capacity and free energy analyses. Furthermore, the equation of state in the pressure-horizon radius plane reveals -dependent critical behavior, consistent with the extended phase space analysis. The complete agreement among canonical, extended, and geometric thermodynamic diagnostics demonstrates that the -induced branches correspond to physically distinct phases, providing a robust, -dependent extension of the thermodynamic and phase structure of the Bardeen-AdS black hole.
© The Author(s) 2026
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3.
