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The universal Ehrenfest scheme on black holes

Li-Chun Zhang

Institute of Theoretical Physics, Shanxi Datong University, Datong 037009, P. R. China

E-mail Address: mameng_1984@163.com

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and

Ren Zhao

Institute of Theoretical Physics, Shanxi Datong University, Datong 037009, P. R. China

E-mail Address: zhao2969@sina.com

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https://doi.org/10.1142/S0217732315501874Cited by:2 (Source: Crossref)

Abstract

By use of the Jacobi determinant, we verify that, for a thermodynamic system which satisfies the first law of thermodynamics, if only there is second-order phase transition in the system, the Prigogine–Defay ratio is the constant 1. This conclusion is universal and independent of the concrete forms of the thermodynamic functions and also apply to black holes.

Keywords:

PACS: 04.70.Dy

References

1. J. D. Bekenstein, Lett. Nuovo Cimento 4, 737 (1972). Crossref, Web of Science, ADS, Google Scholar
2. J. D. Bekenstein, Phys. Rev. D 9, 3292 (1974). Crossref, Web of Science, ADS, Google Scholar
3. J. M. Bardeen, B. Carter and S. W. Hawking, Commun. Math. Phys. 31, 161 (1973). Crossref, Web of Science, ADS, Google Scholar
4. S. W. Hawking, Commun. Math. Phys. 43, 199 (1975). Crossref, Web of Science, ADS, Google Scholar
5. S. Hawking and D. N. Page, Commun. Math. Phys. 87, 577 (1983). Crossref, Web of Science, ADS, Google Scholar
6. A. Chamblin, R. Emparan, C. Johnson and R. Myers, Phys. Rev. D 60, 064018 (1999). Crossref, Web of Science, ADS, Google Scholar
7. A. Chamblin, R. Emparan, C. Johnson and R. Myers, Phys. Rev. D 60, 104026 (1999). Crossref, Web of Science, ADS, Google Scholar
8. B. P. Dolan, Class. Quantum Grav. 28, 125020 (2011). Crossref, Web of Science, ADS, Google Scholar
9. B. P. Dolan, Phys. Rev. D 84, 127503 (2011). Crossref, Web of Science, ADS, Google Scholar
10. M. Cvetic, G. W. Gibbons, D. Kubiznak and C. N. Pope, Phys. Rev. D 84, 024037 (2011). Crossref, Web of Science, ADS, Google Scholar
11. D. Kubiznak and R. B. Mann, JHEP 1207, 033 (2012). Crossref, Web of Science, ADS, Google Scholar
12. S. Gunasekaran, D. Kubiznak and R. B. Mann, JHEP 2012, 1 (2012). Crossref, Web of Science, Google Scholar
13. B. P. Dolan, D. Kastor, D. Kubiznak, R. B. Mann and J. Traschen, Phys. Rev. D 87, 104017 (2013). Crossref, Web of Science, ADS, Google Scholar
14. S.-W. Wei and Y.-X. Liu, Phys. Rev. D 87, 044014 (2013). Crossref, Web of Science, ADS, Google Scholar
15. R.-G. Cai, L.-M. Cao, L. Li and R.-Q. Yang, JHEP 1309, 005 (2013). Crossref, Web of Science, ADS, Google Scholar
16. S. H. Hendi and M. H. Vahidinia, Phys. Rev. D 88, 084045 (2013). Crossref, Web of Science, ADS, Google Scholar
17. D.-C. Zou, Y. Liu, B. Wang and W. Xu, Phys. Rev. D 90, 104035 (2014). Crossref, Web of Science, ADS, Google Scholar
18. R. Zhao, H.-H. Zhao, M.-S. Ma and L.-C. Zhang, Eur. Phys. J. C 73, 2645 (2013). Crossref, Web of Science, ADS, Google Scholar
19. M.-S. Ma and R. Zhao, Phys. Rev. D 89, 044005 (2014). Crossref, Web of Science, ADS, Google Scholar
20. M.-S. Ma, Phys. Lett. B 735, 45 (2014). Crossref, Web of Science, ADS, Google Scholar
21. D.-C. Zou, S.-J. Zhang and B. Wang, Phys. Rev. D 89, 044002 (2014). Crossref, Web of Science, ADS, Google Scholar
22. W. Xu, H. Xu and L. Zhao, Eur. Phys. J. C 74, 2970 (2014). Crossref, Web of Science, ADS, Google Scholar
23. H.-H. Zhao, L.-C. Zhang, M.-S. Ma and R. Zhao, Phys. Rev. D 90, 064018 (2014). Crossref, Web of Science, ADS, Google Scholar
24. L.-C. Zhang, M.-S. Ma, H.-H. Zhao and R. Zhao, Eur. Phys. J. C 74, 3052 (2014). Crossref, Web of Science, ADS, Google Scholar
25. M.-S. Ma, H.-H. Zhao, L.-C. Zhang and R. Zhao, Int. J. Mod. Phys. A 29, 1450050 (2014). Link, Web of Science, ADS, Google Scholar
26. R. Zhao, M.-S. Ma, H.-H. Zhao and L.-C. Zhang, Adv. High Energy Phys. 2014, 124854 (2014). Crossref, Web of Science, Google Scholar
27. R. Banerjee, S. K. Modak and D. Roychowdhury, JHEP 1210, 125 (2012). Crossref, Web of Science, ADS, Google Scholar
28. R. Banerjee, S. K. Modak and S. Samanta, Phys. Rev. D 84, 064024 (2011). Crossref, Web of Science, ADS, Google Scholar
29. J.-X. Mo and W.-B. Liu, Phys. Lett. B 727, 336 (2013). Crossref, Web of Science, ADS, Google Scholar
30. J.-X. Mo, G.-Q. Li and W.-B. Liu, Phys. Lett. B 730, 111 (2014). Crossref, Web of Science, ADS, Google Scholar
31. J.-X. Mo and W.-B. Liu, Phys. Rev. D 89, 084057 (2014). Crossref, Web of Science, ADS, Google Scholar
32. J.-X. Mo, X.-X. Zeng, G.-Q. Li, X. Jiang and W.-B. Liu, JHEP 1310, 056 (2013). Crossref, Web of Science, ADS, Google Scholar