Necessity of q-expectation value in nonextensive statistical mechanics

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

Volumn 71, Issue 1, 2005, Pages

  Abe, Sumiyoshi ^a   Bagci, G B ^b  

^a UNIVERSITY OF TSUKUBA   (Japan)

^b MIDDLE EAST TECHNICAL UNIVERSITY   (Turkey)

Author keywords

[No Author keywords available]

Indexed keywords

COMPLEX NETWORKS; EXPECTATION VALUES; NONEXTENSIVE STATISTICAL MECHANICS; RANDOM VARIABLES;

ENTROPY; LAGRANGE MULTIPLIERS; LINEAR ALGEBRA; MATHEMATICAL TRANSFORMATIONS; PROBABILITY DISTRIBUTIONS; THEOREM PROVING; THERMODYNAMICS; VALUE ENGINEERING;

STATISTICAL MECHANICS;

EID: 37649030585     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.71.016139     Document Type: Article

References (68)

1. Special issue of Braz. J. Phys. 29 (1999), edited by S. R. A. Salinas and C. Tsallis.
2. Nonextensive Statistical Mechanics and its Applications, edited by S. Abe and Y. Okamoto (Springer-Verlag, Heidelberg, 2001).
3. Special issue of Physica A305(1,2) (2002), edited by G. Kaniadakis, M. Lissia, and A. Rapisarda.
4. Nonextensive Entropy - Interdisciplinary Applications, edited by M. Gell-Mann and C. Tsallis (Oxford University Press, New York, 2004).
5. C. Tsallis, J. Stat. Phys. 52, 479 (1988).
6. V. Latora, M. Baranger, A. Rapisarda, and C. Tsallis, Phys. Lett. A 273, 97 (2000).
7. F. A. B. F. de Moura, U. Tirnakli, and M. L. Lyra, Phys. Rev. E 62, 6361 (2000).
8. F. Baldovin and A. Robledo, Phys. Rev. E 66, 045104 (2002); Europhys. Lett. 60, 518 (2002).
9. F. Baldovin and A. Robledo, Phys. Rev. E 66, 045104 (2002); Europhys. Lett. 60, 518 (2002).
10. R. S. Johal and U. Tirnakli, Physica A 331, 487 (2004).
11. B. M. Boghosian, P. J. Love, P. V. Coveney, I. V. Karlin, S. Succi, and J. Yepez, Phys. Rev. E 68, 025103 (2003).
12. M. S. Reis, J. C. C. Freitas, M. T. D. Orlando, E. K. Lenzi, and I. S. Oliveira, Europhys. Lett. 58, 42 (2002).
13. D. B. Walton and J. Rafelski, Phys. Rev. Lett. 84, 31 (2000).
14. I. Bediaga, E. M. F. Curado, and J. M. de Miranda, Physica A 286, 156 (2000).
15. C. Beck, Physica A 286, 164 (2000).
16. W. M. Alberico, A. Lavagno, and P. Quarati, Eur. Phys. J. C 12, 499 (2000).
17. F. S. Navarra, O. V. Utyuzh, G. Wilk, and Z. Wlodarczyk, Phys. Rev. D 67, 114002 (2003).
18. C. Tsallis, J. C. Anjos, and E. P. Borges, Phys. Lett. A 310, 372 (2003).
19. A. Upadhyaya, J. P. Rieu, J. A. Glazier, and Y. Sawada, Physica A 293, 549 (2001).
20. D. Prato and C. Tsallis, Phys. Rev. E 60, 2398 (1999).
21. S. Abe and A. K. Rajagopal, J. Phys. A 33, 8723 (2000).
22. E. Lutz, Phys. Rev. A 67, 051402 (2003); see also S. Abe, Phys. Rev. E 69, 016102 (2004).
23. E. Lutz, Phys. Rev. A 67, 051402 (2003); see also S. Abe, Phys. Rev. E 69, 016102 (2004).
24. A. Lavagno, G. Kaniadakis, M. Rego-Monteiro, P. Quarati, and C. Tsallis, Astrophys. Lett. Commun. 35, 449 (1998).
25. A. Taruya and M. Sakagami, Physica A 322, 285 (2003); Phys. Rev. Lett. 90, 181101 (2003).
26. A. Taruya and M. Sakagami, Physica A 322, 285 (2003); Phys. Rev. Lett. 90, 181101 (2003).
27. L. Borland, Phys. Rev. Lett. 89, 098701 (2002); Quant. Finance 2, 415 (2002).
28. L. Borland, Phys. Rev. Lett. 89, 098701 (2002); Quant. Finance 2, 415 (2002).
29. N. Kozuki and N. Fuchikami, Physica A 329, 222 (2003).
30. A. Rossani and A. M. Scarfone, Physica A 282, 212 (2000).
31. S. Abe and N. Suzuki, Phys. Rev. E 67, 016106 (2003).
32. S. Abe, N. Suzuki, J. Geophys. Res. 108(B2), 2113 (2003); Physica A (to be published).
33. S. Abe, N. Suzuki, J. Geophys. Res. 108(B2), 2113 (2003); Physica A (to be published).
34. O. Sotolongo-Costa and A. Posadas, Phys. Rev. Lett. 92, 048501 (2004).
35. B. Tadic and S. Thurner, Physica A 332, 566 (2004).
36. S. Abe and N. Sukuki, Europhys. Lett. 65, 581 (2004).
37. G. Wilk and Z. Wlodarczyk, Acta Phys. Pol. B 35, 871 (2004).
38. C. Tsallis, R. S. Mendes, and A. R. Plastino, Physica A 261, 534 (1998).
39. C. Beck and F. Schlögl, Thermodynamics of Chaotic Systems An Introduction (Cambridge University Press, Cambridge, England, 1993); S. Abe, Phys. Rev. E 68, 031101 (2003).
40. C. Beck and F. Schlögl, Thermodynamics of Chaotic Systems An Introduction (Cambridge University Press, Cambridge, England, 1993); S. Abe, Phys. Rev. E 68, 031101 (2003).
41. S. Abe and A. K. Rajagopal, J. Phys. A 33, 8733 (2000).
42. T. Wada and A. M. Scarfone, e-print cond-mat/0410527.
43. A. G. Bashkirov, Physica A 340, 153 (2004).
44. S. Abe, Physica A 300, 417 (2001); see also S. Abe, S. Martinez, F. Pennini, and A. Plastino, Phys. Lett. A 281, 126 (2001).
45. S. Abe, Physica A 300, 417 (2001); see also S. Abe, S. Martinez, F. Pennini, and A. Plastino, Phys. Lett. A 281, 126 (2001).
46. J. Naudts, Rev. Math. Phys. 16, 809 (2004).
47. L. M. Bregman, USSR Comput. Math. Math. Phys. 7, 200 (1967).
48. S. Abe, in Proceedings of the 5th International Wigner Symposium, Vienna, 1997, edited by P. Kasperkovitz and D. Grau (World Scientific, Singapore, 1998), p. 66; see also A. K. Rajagopal and S. Abe, Phys. Rev. Lett. 83, 1711 (1999).
49. S. Abe, in Proceedings of the 5th International Wigner Symposium, Vienna, 1997, edited by P. Kasperkovitz and D. Grau (World Scientific, Singapore, 1998), p. 66; see also A. K. Rajagopal and S. Abe, Phys. Rev. Lett. 83, 1711 (1999).
50. C. Tsallis, Phys. Rev. E 58, 1442 (1998).
51. L. Borland, A. R. Plastino, and C. Tsallis, J. Math. Phys. 39, 6490 (1998); 40, 2196(E) (1999).
52. L. Borland, A. R. Plastino, and C. Tsallis, J. Math. Phys. 39, 6490 (1998); 40, 2196(E) (1999).
53. I. Csiszár, Period. Math. Hung. 2, 191 (1972).
54. S. Abe, Phys. Lett. A 224, 326 (1997); 244, 229 (1998); Phys. Rev. A 68, 032302 (2003).
55. S. Abe, Phys. Lett. A 224, 326 (1997); 244, 229 (1998); Phys. Rev. A 68, 032302 (2003).
56. S. Abe, Phys. Lett. A 224, 326 (1997); 244, 229 (1998); Phys. Rev. A 68, 032302 (2003).
57. S. Abe and A. K. Rajagopal, Phys. Rev. Lett. 91, 120601 (2003).
58. S. Abe, Phys. Lett. A 312, 336 (2003); 324, 507(E) (2004); Physica A 344, 359 (2004).
59. S. Abe, Phys. Lett. A 312, 336 (2003); 324, 507(E) (2004); Physica A 344, 359 (2004).
60. S. Abe, Phys. Lett. A 312, 336 (2003); 324, 507(E) (2004); Physica A 344, 359 (2004).
61. C. Tsallis, in Nonextensive Statistical Mechanics and its Applications (Ref. [2]); see also S. Abe, Phys. Rev. E 63, 061105 (2001).
62. C. Tsallis, in Nonextensive Statistical Mechanics and its Applications (Ref. [2]); see also S. Abe, Phys. Rev. E 63, 061105 (2001).
63. J. E. Shore and R. W. Johnson, IEEE Trans. Inf. Theory IT-26, 26 (1980); IT-27, 472 (1981); IT-29, 942 (1983).
64. J. E. Shore and R. W. Johnson, IEEE Trans. Inf. Theory IT-26, 26 (1980); IT-27, 472 (1981); IT-29, 942 (1983).
65. J. E. Shore and R. W. Johnson, IEEE Trans. Inf. Theory IT-26, 26 (1980); IT-27, 472 (1981); IT-29, 942 (1983).
66. J. Uffink, Stud. Hist. Philos. Mod. Phys. 26B, 223 (1995).
67. R. J. V. dos Santos, J. Math. Phys. 38, 4104 (1997); S. Abe, Phys. Lett. A 271, 74 (2000).
68. R. J. V. dos Santos, J. Math. Phys. 38, 4104 (1997); S. Abe, Phys. Lett. A 271, 74 (2000).