Thermodynamic stability and geometric thermodynamics of regular Bardeen AdS black hole using Kaniadakis statistics

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 κ -deformed entropy. By varying both the Kaniadakis parameter κ and the black hole parameters, we uncover additional κ -dependent thermodynamic branches, singularities, and divergence points that are absent in the standard (= 0 κ = 0) 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 κ -dependent critical behavior, consistent with the extended phase space analysis. The complete agreement among canonical, extended, and geometric thermodynamic diagnostics demonstrates that the κ -induced branches correspond to physically distinct phases, providing a robust, κ -dependent extension of the thermodynamic and phase structure of the Bardeen-AdS black hole.