The impact of non-expansive entropies on thermodynamics of high order correction of Schwarzschild-AdS black hole in non-commutative geometry
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".