Thermodynamic aspects of higher-dimensional black holes in Einstein–Gauss–Bonnet gravity through exponential entropy

Abstract We assume exponential corrections to the entropy of 5D charged AdS black hole solutions, which are derived within the framework of Einstein–Gauss–Bonnet gravity and nonlinear electrodynamics. Additionally, we consider two distinct versions of 5D charged AdS black holes by setting the parameters q → 0 and k → 0 (where q represents the charge, and k is the non-linear parameter). We investigate these black holes in the extended phase space, where the cosmological constant is interpreted as pressure, demonstrating the first law of black hole thermodynamics. The focus extends to understanding the thermal stability or instability, as well as identifying first and second-order phase transitions. This exploration is carried out through the analysis of various thermodynamic quantities, including heat capacity at constant pressure, Gibbs free energy (GFE), Helmholtz free energy (HFE), and the trace of the Hessian matrix. In order to visualize phase transitions, identify critical points, analyze stability and provide comprehensive analysis, we have made the contour plot of the mentioned thermodynamic quantities and observed that our results are very consistent. These investigations are conducted within the context of exponentially corrected entropies, providing valuable insights into the intricate thermodynamic behavior of these 5D charged AdS black holes under different parameter limits.