Thermodynamic stability and geometric thermodynamics of Euler Heisenberg black hole using Rényi statistics

Abstract In this study, we investigate the thermodynamic stability and geometric thermodynamics of the Euler–Heisenberg black hole within the Rényi entropy framework. By varying the Rényi parameter as well as the thermodynamic parameters of the system, the stability graphs are analyzed. We observe that the introduction of the Rényi parameter $$\lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>λ</mml:mi> </mml:math> modifies the graph branches, singularities, and stability ranges compared to the Gibbs–Boltzmann statistics. Similar results are obtained upon varying the thermodynamic parameters of the system. We discuss the thermodynamic geometry by employing the HPEM metric to explore the thermal phases and analyze them using two approaches: Rényi and Gibbs–Boltzmann. Our analysis reveals that the divergence points coincide or completely align with the phase transition points.