Look Beyond Additivity and Extensivity of Entropy for Black Hole and Cosmological Horizons
Abstract
1. Introduction
2. Boltzmann–Gibbs Thermodynamics and Statistical Mechanics
2.1. Additivity
2.2. Extensivity
2.3. Concavity
3. Beyond Boltzmann–Gibbs Thermodynamics
3.1. Composability
3.2. Beyond Additivity
3.3. Beyond Extensivity
4. A Comparable Analysis of Nonextensive Entropy Plethora
4.1. Bekenstein Entropy
4.2. Tsallis q, Tsallis–Cirto , Tsallis , and Tsallis–Jensen Entropies
4.2.1. Tsallis q-Entropy
4.2.2. Rényi Entropy
4.2.3. Tsallis–Cirto -Entropy
4.2.4. Tsallis -Entropy
4.2.5. Tsallis–Jensen -Entropy
4.3. Barrow Fractal Horizon -Entropy and Its Relation to Bekenstein and Tsallis–Cirto -Entropy
4.4. Landsberg U-Entropy
4.5. Sharma–Mittal Entropy
4.6. Kaniadakis Entropy
4.7. Thermal Equilibrium Temperature vs. Equilibrium Temperature for Nonextensive Entropies
4.8. Classification of Entropies
4.9. Generalized Four- and Five-Parameter Entropic Forms
5. Summary and Discussion
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Equivalent Forms of Tsallis q-Entropy
Appendix B. Validity of Abé Composition Rule for Tsallis q−Entropy and Landsberg U−Entropy
Appendix C. Validity of Abé Composition Rule for Sharma–Mittal Entropy
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Entropy Type | Extensivity | Additivity | Abé Addition Rule | -Addition Rule |
---|---|---|---|---|
Boltzmann–Gibbs | yes | yes | yes, | yes, |
Tsallis | no | no | yes, | no |
Tsallis–Cirto | no | no | no | yes |
General Tsallis | no | no | no | no |
Tsallis–Jensen | no | no | no | yes, |
Entropy Type | Extensivity | Additivity | Abé Rule | -Rule | K-Rule |
---|---|---|---|---|---|
Boltzmann–Gibbs | yes | yes | yes, | yes, | yes, |
Bekenstein | no | no * | no | no | no |
Tsallis q-entropy | no | no | yes, | no | no |
Tsallis–Cirto | no | no | no | yes | no |
Tsallis–Cirto | yes | no | no | yes, | no |
Barrow | no | no * | no | no | no |
Barrow | no | no | no | yes | no |
Barrow ( | yes | no | no | yes, | no |
Rényi | no | yes | yes, | no | no |
Landsberg U-entropy | no | no | yes, | no | no |
Kaniadakis | no | no | no | no | yes |
Sharma–Mittal | no | no | yes, | no | no |
Tsallis -entropy | no | no | no | no | no |
Tsallis–Jensen | no | no | no | yes, | no |
Tsallis–Jensen | no | no | no | yes, | no |
Tsallis–Jensen | no | yes | yes, | no | no |
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Da̧browski, M.P. Look Beyond Additivity and Extensivity of Entropy for Black Hole and Cosmological Horizons. Entropy 2024, 26, 814. https://doi.org/10.3390/e26100814
Da̧browski MP. Look Beyond Additivity and Extensivity of Entropy for Black Hole and Cosmological Horizons. Entropy. 2024; 26(10):814. https://doi.org/10.3390/e26100814
Chicago/Turabian StyleDa̧browski, Mariusz P. 2024. "Look Beyond Additivity and Extensivity of Entropy for Black Hole and Cosmological Horizons" Entropy 26, no. 10: 814. https://doi.org/10.3390/e26100814
APA StyleDa̧browski, M. P. (2024). Look Beyond Additivity and Extensivity of Entropy for Black Hole and Cosmological Horizons. Entropy, 26(10), 814. https://doi.org/10.3390/e26100814