Nonadditive entropy reconciles the area law in quantum systems with classical thermodynamics

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 78, Issue 2, 2008, Pages

  Caruso, Filippo ^a   Tsallis, Constantino ^b,c  

^a INFM   (Italy)

^b CENTRO BRASILEIRO DE PESQUISAS FÍSICAS   (Brazil)

^c SANTA FE INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICS; LAWS AND LEGISLATION; MATHEMATICAL MODELS; QUANTUM ELECTRONICS; QUANTUM OPTICS; QUANTUM THEORY; THERMODYNAMICS;

BLACK HOLES; BOLTZMANN; CLASSICAL THERMODYNAMICS; D-DIMENSIONAL QUANTUM SYSTEMS; ENTROPIC INDEXES; LINEAR SIZE; MATHEMATICAL MODELLING; QUANTUM SYSTEMS; VON NEUMANN ENTROPY;

ENTROPY;

EID: 49449111151     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.78.021102     Document Type: Article

References (59)

1. C. Tsallis, M. Gell-Mann, and Y. Sato, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.0503807102 102, 15377 (2005).
2. C. Tsallis, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01016429 52, 479 (1988).
3. C. Tsallis, in Encyclopedia of Complexity and Systems Science (Springer, Berlin, in press);
4. C. Tsallis in Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World (Springer, Berlin, in press).
5. Nonextensive Entropy: Interdisciplinary Applications, edited by, M. Gell-Mann, and, C. Tsallis, (Oxford University Press, New York, 2004).
6. Nonextensive Statistical Mechanics: New Trends, New Perspectives, edited by, J. P. Boon, and, C. Tsallis, special issue of Europhys. News 36, 6 (2005). 0531-7479
7. J. Havrda and F. Charvat, Kybernetika KYBNAI 0023-5954 3, 30 (1967)
8. Z. Daróczy, Infect. Control 16, 36 (1970) 0195-9417
9. J. Lindhard and V. Nielsen, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. KDVSAK 0023-3323 38 (9), 1 (1971).
10. S. Umarov, C. Tsallis, and S. Steinberg, Milan J. Math. (to be published).
11. P. Douglas, S. Bergamini, and F. Renzoni, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.110601 96, 110601 (2006).
12. B. Liu and J. Goree, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.055003 100, 055003 (2008).
13. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, U.K., 2000).
14. A. Osterloh, L. Amico, G. Falci, and R. Fazio, Nature (London) NATUAS 0028-0836 10.1038/416608a 416, 608 (2002).
15. T. J. Osborne and M. A. Nielsen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.032110 66, 032110 (2002).
16. G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.227902 90, 227902 (2003).
17. A. R. Its, B.-Q. Jin, and V. E. Korepin, J. Phys. A 38, 2975 (2005). 0022-3689
18. J. I. Latorre, E. Rico, and G. Vidal, Quantum Inf. Comput. QICUAW 1533-7146 10.1103/PhysRevLett.90.227902 4, 48 (2004).
19. L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.80.517 80, 517 (2008).
20. T. Barthel, M. C. Chung, and U. Schollwock, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.022329 74, 022329 (2006).
21. M. B. Plenio, J. Eisert, J. Dreißig, and M. Cramer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.060503 94, 060503 (2005)
22. M. Cramer, J. Eisert, M. B. Plenio, and J. Dreißig, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.012309 73, 012309 (2006).
23. L. Bombelli, R. K. Koul, J. Lee, and R. D. Sorkin, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.34.373 34, 373 (1986).
24. M. Srednicki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71. 666 71, 666 (1993).
25. (a) J. M. Bardeen, B. Carter, and S. W. Hawking, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01645742 31, 161 (1973)
26. (b) J. D. Bekenstein, Lett. Nuovo Cimento Soc. Ital. Fis. LNUCAE 0375-930X 10.1007/BF02757029 4, 737 (1972)
27. J. D. Bekenstein, (c) Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.7. 2333 7, 2333 (1973)
28. (d) G. 't Hooft, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(85) 90418-3 256, 727 (1985)
29. (e) C. G. Callan and F. Wilczek, Phys. Lett. B PYLBAJ 0370-2693 10.1016/0370-2693(94)91007-3 333, 55 (1994)
30. (f) D. Kabat and M. J. Strassler, Phys. Lett. B PYLBAJ 0370-2693 10.1016/0370-2693(94)90515-0 329, 46 (1994)
31. (g) J. D. Bekenstein, Contemp. Phys. CTPHAF 0010-7514 10.1080/00107510310001632523 45, 31 (2004).
32. K. Zyczkowski and I. Bengtsson, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1006/aphy.2001.6201 295, 115 (2002).
33. C. Brukner and A. Zeilinger, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.022113 63, 022113 (2001).
34. F. Giraldi and P. Grigolini, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.032310 64, 032310 (2001).
35. C. Tsallis, S. Lloyd, and M. Baranger, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.042104 63, 042104 (2001);
36. S. Abe and A. K. Rajagopal, Physica A PHYADX 0378-4371 10.1016/S0378-4371(00)00476-3 289, 157 (2001).
37. S. Abe and A. K. Rajagopal, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.60.3461 60, 3461 (1999)
38. S. Abe, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.052323 65, 052323 (2002).
39. A. K. Rajagopal and R. W. Rendell, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.022322 72, 022322 (2005).
40. M. B. Plenio and S. Virmani, Quantum Inf. Comput. QICUAW 1533-7146 7, 1 (2007).
41. A. Popescu, A. J. Short, and A. Winter, Nat. Phys. ZZZZZZ 1745-2473 2, 754 (2006).
42. F. Mintert and K. Zyczkowski, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.022317 69, 022317 (2004).
43. E. Lieb, T. Schultz, and D. Mattis, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(61)90115-4 16, 407 (1961).
44. P. Pfeuty, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(70)90270- 8 57, 79 (1970).
45. E. Barouch, B. M. McCoy, and M. Dresden, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.2.1075 2, 1075 (1970)
46. E. Barouch and B. M. McCoy, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.3.786 3, 786 (1971).
47. F. Caruso and C. Tsallis, in Complexity, Metastability and Nonextensivity, edited by, S. Abe, H.J. Herrmann, P. Quarati, A. Rapisarda, and, C. Tsallis, AIP Conf. Proc. No. 965 (AIP, Melville, NY, 2007), p. 51.
48. C. Anteneodo and C. Tsallis, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.5313 80, 5313 (1998).
49. A. Pluchino, A. Rapisarda, and C. Tsallis, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/80/26002 80, 26002 (2007).
50. R. Savit, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.52.453 52, 453 (1980).
51. P. Calabrese and J. Cardy, J. Stat. Mech.: Theory Exp. ZZZZZZ 1742-5468 (2004) P06002;
52. C. Holzhey, F. Larsen, and F. Wilczek, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(94)90402-2 424, 443 (1994).
53. A. Robledo, Mol. Phys. MOPHAM 0026-8976 10.1080/00268970500185989 103, 3025 (2005).
54. B.-Q. Jin and V. E. Korepin, J. Stat. Phys. JSTPBS 0022-4715 10.1023/B:JOSS.0000037230.37166.42 116, 79 (2004).
55. F. Franchini, A. R. Its, and V. E. Korepin, J. Phys. A JPHAC5 0305-4470 10.1088/1751-8113/41/2/025302 41, 025302 (2008).
56. V. Eisler, A. Legeza, and Z. Racz, J. Stat. Mech.: Theory Exp. ZZZZZZ 1742-5468 (2006) P11013.
57. I. Bediaga, E. M. F. Curado, and J. M. de Miranda, Physica A PHYADX 0378-4371 10.1016/S0378-4371(00)00368-X 286, 156 (2000).
58. R. Bousso, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.825 74, 825 (2002).
59. http://tsallis.cat.cbpf.br/biblio.htm