Jafar Sadeghi, Behnam Pourhassan, Fatemeh Khosravani
This work examines the thermodynamics of Schwarzschild–AdS black holes by introducing higher-order corrections within a noncommutative spacetime framework and by employing several non-extensive entropy formalisms. Modeling the black hole mass using a Lorentzian distribution captures the smeared structure of spacetime, and solving the modified Einstein equations with a negative cosmological constant leads to a generalized, nonclassical black hole solution. Because standard statistical mechanics do not fully account for the long-range and nonlocal features inherent to gravitational systems, we turn to generalized entropy models, Tsallis, Rényi, and Barrow, which incorporate such effects, along with possible quantum-gravity–motivated deformations. Our analysis shows that these non-extensive entropies can produce marked departures from the thermodynamic behavior expected from the classical Bekenstein–Hawking framework. Interestingly, when higher-order corrections become dominant, the modified thermodynamic quantities begin to approach those of the classical regime, hinting at an underlying universality that emerges across distinct statistical descriptions. In addition, we investigate the Joule–Thomson expansion in each entropy model to understand how the temperature reacts to pressure variations under isenthalpic (constant-mass) processes. The resulting expressions for the mass, Hawking temperature, heat capacity, and Gibbs free energy reveal subtle differences in stability, phase structure, and critical behavior, all governed by the specific form of the chosen non-extensive entropy. These results deepen our understanding of black hole thermodynamics in a noncommutative, quantum-corrected spacetime and open up new theoretical pathways for exploring gravitational systems beyond traditional frameworks.