Thermodynamics of Deformed AdS-Schwarzschild Black Holes Beyond the Bekenstein Paradigm

Abstract

This work investigates the thermodynamic behavior of deformed AdS-Schwarzschild black holes by incorporating higher-order corrections within non-interacting spacetime models and extended entropy frameworks. To address the inadequacies of classical statistical mechanics in describing gravitational systems with non-local and long-range interactions, we employ non-extensive entropy formalisms, specifically Tsallis and Barrow entropies, which capture quantum-scale deviations and extended correlations. The resulting thermodynamic analysis reveals significant departures from conventional black hole behavior under strong entropy deformations. Notably, as the degree of non-extensivity decreases, the system asymptotically recovers classical features, indicating an emergent universality across statistical regimes. Furthermore, the Joule-Thomson (JT) expansion is examined to analyze the temperature-pressure response during adiabatic processes. Key thermodynamic quantities, including mass, temperature, heat capacity, Gibbs free energy, enthalpy, internal energy, and the JT coefficient, are computed under the influence of non-extensive entropy corrections. These results provide deeper insight into black hole thermodynamics in quantum-corrected spacetimes and offer new avenues for exploring gravitational systems beyond the traditional Bekenstein-Hawking (BH) framework.