Nonextensive Statistical Mechanics and Black Hole Thermodynamics: Tsallis and Kaniadakis Entropies

Document Type : Regular article

Authors

Department of Theoretical Physics, Faculty of Basic Sciences, University of Mazandaran, 47416-95447, Babolsar, Iran

Abstract

We study the impact of nonextensive entropy on the thermodynamics of various black hole configurations, utilizing both Tsallis and Kaniadakis statistical frameworks. Additionally, we explore the stability of these black holes using the framework of nonextensivity. Our analysis reveals that the nonextensive Kaniadakis entropy does not result in any stability for the black holes. In contrast, the nonextensive Tsallis entropy ensures the stability of various black hole configurations.

Keywords

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[1] J. D. Bekenstein, “Black holes and entropy”, Phys. Rev. D 7, 2333 (1973). DOI:10.1103/PhysRevD.7.2333
[2] S. W. Hawking, “Black hole explosions”, Nature 248, 30 (1974). DOI:10.1038/248030a0
[3] P. Chen, Y. C. Ong, and D. h. Yeom, “Black Hole Remnants and the Information Loss Paradox”, Phys. Rept. 603, 1 (2015). DOI:10.1016/j.physrep.2015.10.007
[4] J. M. Bardeen, B. Carter, and S. W. Hawking, “The Four laws of black hole mechanics”, Commun. Math. Phys. 31, 161 (1973). DOI:10.1007/BF01645742
[5] G. W. Gibbons and M. J. Perry, “Black Holes and Thermal Green’s Functions”, Proc. Roy. Soc. Lond. A 358, 467 (1978). DOI:10.1098/rspa.1978.0022
[6] S. W. Hawking and D. N. Page, “Thermodynamics of Black Holes in anti-De Sitter Space”, Commun. Math. Phys. 87, 577 (1983). DOI:10.1007/BF01208266
[7] T. Jacobson, “Thermodynamics of space-time: The Einstein equation of state”, Phys. Rev. Lett. 75, 1260 (1995). DOI:10.1103/PhysRevLett.75.1260
[8] D. Kubiznak and R. B. Mann, “Black hole chemistry”, Can. J. Phys. 93(9), 999 (2015). DOI:10.1139/cjp-2014-0465
[9] M. M. Caldarelli, G. Cognola, and D. Klemm, “Thermodynamics of Kerr-NewmanAdS black holes and conformal field theories”, Class. Quant. Grav. 17, 399 (2000). DOI:10.1088/0264-9381/17/2/310
[10] R. G. Cai and S. P. Kim, “First law of thermodynamics and Friedmann equations of Friedmann-Robertson-Walker universe”, JHEP 02, 050 (2005). DOI:10.1088/1126-6708/2005/02/050
[11] P. C. W. Davies, “Thermodynamics of Black Holes”, Proc. Roy. Soc. Lond. A 353, 499 (1977). DOI:10.1098/rspa.1977.0047
[12] D. A. Easson, P. H. Frampton, and G. F. Smoot, “Entropic Accelerating Universe”, Phys. Lett. B 696, 273 (2011). DOI:10.1016/j.physletb.2010.12.025
[13] S. W. Hawking, “Gravitational radiation from colliding black holes”, Phys. Rev. Lett. 26, 1344 (1971). DOI:10.1103/PhysRevLett.26.1344
[14] C. Tsallis, “Possible Generalization of Boltzmann-Gibbs Statistics”, J. Statist. Phys. 52, 479 (1988). DOI:10.1007/BF01016429
[15] C. Tsallis, R. S. Mendes, and A. R. Plastino, “The Role of constraints within generalized nonextensive statistics”, Physica A 261, 534 (1998). DOI:10.1016/S0378-4371(98)00437-3
[16] M. Nauenberg, “Critique of q-entropy for thermal statistics”, Phys. Rev. E 67, 036114 (2003). DOI:10.1103/PhysRevE.67.036114
[17] A. S. Parvan and T. S. Biro, “Extensive Renyi statistics from non-extensive entropy”, Phys. Lett. A 340, 375 (2005). DOI:10.1016/j.physleta.2005.04.036
[18] C. Tsallis and L. J. L. Cirto, “Black hole thermodynamical entropy”, Eur. Phys. J. C 73, 2487 (2013). DOI:10.1140/epjc/s10052-013-2487-6
[19] T. S. Biró and V. G. Czinner, “A q-parameter bound for particle spectra based on black hole thermodynamics with Rényi entropy”, Phys. Lett. B 726, 861 (2013). DOI:10.1016/j.physletb.2013.09.032
[20] V. G. Czinner, “Black hole entropy and the zeroth law of thermodynamics”, Int. J. Mod. Phys. D 24(09), 1542015 (2015). DOI:10.1142/S0218271815420158
[21] V. G. Czinner and H. Iguchi, “Thermodynamics, stability and Hawking–Page transition of Kerr black holes from Rényi statistics”, Eur. Phys. J. C 77(12), 892 (2017). DOI:10.1140/epjc/s10052-017-5453-x
[22] C. Tsallis, “Black Hole Entropy: A Closer Look”, Entropy 22(1), 17 (2019). DOI:10.3390/e22010017
[23] G. Kaniadakis, “Statistical mechanics in the context of special relativity”, Phys. Rev. E 66, 056125 (2002). DOI:10.1103/PhysRevE.66.056125
[24] G. Kaniadakis, “Statistical mechanics in the context of special relativity. II.”, Phys. Rev. E 72, 036108 (2005). DOI:10.1103/PhysRevE.72.036108
[25] J. D. Barrow, “The Area of a Rough Black Hole”, Phys. Lett. B 808, 135643 (2020). DOI:10.1016/j.physletb.2020.135643
[26] S. Nojiri, S. D. Odintsov, and V. Faraoni, “Area-law versus Rényi and Tsallis black hole entropies”, Phys. Rev. D 104(8), 084030 (2021). DOI:10.1103/PhysRevD.104.084030
[27] C. Promsiri, E. Hirunsirisawat, and W. Liewrian, “Thermodynamics and Van der Waals phase transition of charged black holes in flat spacetime via Rényi statistics”, Phys. Rev. D 102(6), 064014 (2020). DOI:10.1103/PhysRevD.102.064014
[28] M. P. Dabrowski and V. Salzano, “Geometrical observational bounds on a fractal horizon holographic dark energy”, Phys. Rev. D 102(6), 064047 (2020). DOI:10.1103/PhysRevD.102.064047
[29] A. Majhi, “Non-extensive Statistical Mechanics and Black Hole Entropy From Quantum Geometry”, Phys. Lett. B 775, 32 (2017). DOI:10.1016/j.physletb.2017.10.043
[30] G. G. Luciano and M. Blasone, “q-generalized Tsallis thermostatistics in Unruh effect for mixed fields”, Phys. Rev. D 104(4), 045004 (2021). DOI:10.1103/PhysRevD.104.045004
[31] M. Asghari and A. Sheykhi, “Observational constraints of the modified cosmology through Barrow entropy”, Eur. Phys. J. C 82(5), 388 (2022). DOI:10.1140/epjc/s10052-022-10262-8
[32] E. M. C. Abreu and J. A. Neto, “Statistical approaches and the Bekenstein bound conjecture in Schwarzschild black holes”, Phys. Lett. B 835, 137565 (2022). DOI:10.1016/j.physletb.2022.137565
[33] A. Sayahian Jahromi, S. A. Moosavi, H. Moradpour, J. P. Morais Graça, I. P. Lobo, I. G. Salako, and A. Jawad, “Generalized entropy formalism and a new holographic dark energy model”, Phys. Lett. B 780, 21 (2018). DOI:10.1016/j.physletb.2018.02.052
[34] N. Drepanou, A. Lymperis, E. N. Saridakis, and K. Yesmakhanova, “Kaniadakis holographic dark energy and cosmology”, Eur. Phys. J. C 82(5), 449 (2022). DOI:10.1140/epjc/s10052-022-10415-9
[35] B. Pourhassan and İ. Sakallı, “Non-perturbative correction to the Hořava–Lifshitz black hole thermodynamics”, Chin. J. Phys. 79, 322 (2022). DOI:10.1016/j.cjph.2022.09.006
[36] S. Sen, A. Saha, and S. Gangopadhyay, “Signatures of quantum geometry from exponential corrections to the black hole entropy”, Gen. Rel. Grav. 56(5), 57 (2024). DOI:10.1007/s10714-024-03241-9
[37] B. Pourhassan, M. Dehghani, S. Upadhyay, I. Sakalli, and D. V. Singh, “Exponential corrected thermodynamics of Born–Infeld BTZ black holes in massive gravity”, Mod. Phys. Lett. A 37(33n34), 2250230 (2022). DOI:10.1142/S0217732322502303
[38] S. Soroushfar, B. Pourhassan, and İ. Sakallı, “Exploring non-perturbative corrections in thermodynamics of static dirty black holes”, Phys. Dark Univ. 44, 101457 (2024). DOI:10.1016/j.dark.2024.101457
[39] G. Maiella and C. Stornaiolo, “A CFT description of the BTZ black hole: Topology versus geometry (or thermodynamics versus statistical mechanics”, Int. J. Mod. Phys. A 22, 3429 (2007). DOI:10.1142/S0217751X07037111
[40] Rényi and Alfréd “On the dimension and entropy of probability distributions”, Acta Mathematica Academiae Scientiarum Hungarica 10(1-2), (1959). DOI:10.1007/BF02063299
[41] P. K. Townsend, “Black holes: Lecture notes”, [arXiv:gr-qc/9707012].
[42] S. Carlip, “Black Hole Thermodynamics”, Int. J. Mod. Phys. D 23, 1430023 (2014). DOI:10.1142/S0218271814300237
[43] J. D. Bekenstein, “Statistical Black Hole Thermodynamics”, Phys. Rev. D 12, 3077 (1975) DOI:10.1103/PhysRevD.12.3077
[44] P. C. W. Davies, “Thermodynamics of black holes”, Rept. Prog. Phys. 41, 1313 (1978). DOI:10.1088/0034-4885/41/8/004
[45] M. P. Hobson, G. P. Efstathiou, and A. N. Lasenby, “General Relativity: An Introduction for Physicists”, Cambridge University Press (2006). DOI:10.1017/CBO9780511790904
[46] V. Avramov, H. Dimov, M. Radomirov, R. C. Rashkov, and T. Vetsov, “On Thermodynamic Stability of Black Holes. Part I: Classical Stability”, Eur. Phys. J. C 84(3), 281 (2024). DOI:10.1140/epjc/s10052-024-12639-3
[47] I. Cimidiker, M. P. Dabrowski, and H. Gohar, “Generalized uncertainty principle impact on nonextensive black hole thermodynamics”, Class. Quant. Grav. 40(14), 145001 (2023). DOI:10.1088/1361-6382/acdb40
[48] A. Alonso-Serrano, M. P. Dabrowski, and H. Gohar, “Nonextensive Black Hole Entropy and Quantum Gravity Effects at the Last Stages of Evaporation”, Phys. Rev. D 103(2), 026021 (2021). DOI:10.1103/PhysRevD.103.026021
[49] H. Moradpour, A. H. Ziaie, I. P. Lobo, J. P. Morais Graça, U. K. Sharma, and A. S. Jahromi, “The third law of thermodynamics, non-extensivity and energy definition in black hole physics”, Mod. Phys. Lett. A 37(12), 2250076 (2022). DOI:10.1142/S0217732322500766
[50] S. Rani, A. Jawad, H. Moradpour, and A. Tanveer, “Tsallis entropy inspires geometric thermodynamics of specific black hole”, Eur. Phys. J. C 82(8), 713 (2022). DOI:10.1140/epjc/s10052-022-10655-9
[51] S. Ghaffari, G. G. Luciano, and A. Sheykhi, “Nonextensive entropies impact onto thermodynamics and phase structure of Kerr–Newman black holes”, Phys. Dark Univ. 44, 101447 (2024). DOI:10.1016/j.dark.2024.101447
[52] C. Tsallis, “Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World”, Springer, (2009). DOI:10.1007/978-0-387-85359-8
Volume 4, Issue 3
September 2024
Pages 63-92
  • Receive Date: 08 June 2024
  • Revise Date: 08 August 2024
  • Accept Date: 29 August 2024