We study the thermodynamics of a five-dimensional Einstein–Gauss–Bonnet (EGB) black hole endowed with Barrow’s fractal entropy, motivated by the complementary roles of highcurvature corrections and quantum horizon microstructure. While the Gauss–Bonnet term modifies the classical geometry in strong-gravity regimes, Barrow entropy introduces nonlinear entropy scaling due to Planck-scale fractal deformation of the horizon. The Hawking temperature shows a rise–maximum–decay behavior with Barrow entropy, and increasing the deformation parameter δ and charge Q suppresses the temperature peak, enhancing stability. The specific heat changes sign, indicating a transition from an unstable small-black-hole phase to a stable large Barrow-dominated phase, while the free energy develops a cusp in the F–T plane, confirming a first-order phase transition. Thermodynamic geometry further reveals strong curvature and instability at low entropy and smooth stabilization at high entropy. These results demonstrate that combining Gauss–Bonnet corrections with fractal entropy produces a richer phase structure and offers a consistent framework to probe quantum geometric effects in higherdimensional black holes.
Biswas et al. (Fri,) studied this question.