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