Asymptotically scale-invariant occupancy of phase space makes the entropy Sq extensive

Proceedings of the National Academy of Sciences of the United States of America

Volumn 102, Issue 43, 2005, Pages 15377-15382

  Tsallis, Constantino ^a,b   Gell Mann, Murray ^a   Sato, Yuzuru ^a  

^a SANTA FE INSTITUTE   (United States)

^b CENTRO BRASILEIRO DE PESQUISAS FÍSICAS   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; ENTROPY; MATHEMATICAL MODEL; NONLINEAR SYSTEM; PHYSICS; PRIORITY JOURNAL; STATISTICAL ANALYSIS; THERMODYNAMICS;

EID: 27344449202     PISSN: 00278424     EISSN: None     Source Type: Journal    
DOI: 10.1073/pnas.0503807102     Document Type: Article

References (46)

1. Gell-Mann, M. & Tsallis, C., eds. (2004) Nonextensive Entropy: Interdisciplinary Applications (Oxford Univ. Press, New York), pp. 1-422.
2. Harvda, J. & Charvat, F. (1967) Kybernetica 3, 30-35.
3. Vajda, I. (1968) Kybernetika 4, 105-110 (in Czech).
4. Daroczy, Z. (1970) Inf. Control 16, 36-51.
5. Wehrl, A. (1978) Rev. Mod. Phys. 50, 221-260.
6. Tsallis, C. (1995) Chaos Solitons Fractals 6, 539-559.
7. Abe, S. & Okamoto, Y., eds. (2001) Nonextensive Statistical Mechanics and Its Applications, Lecture Notes in Physics (Springer, Heidelberg).
8. Tsallis, C. (2002) Chaos Solitons Fractals 13, 371-391.
9. Csiszar, I. (1974) in Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, and the European Meeting of Statisticians, 1974 (Reidel, Dordrecht), pp. 73-86.
10. Schutzenberger, P.-M. (1954) Publ. Inst. Statist. Univ. Paris 3, 3.
11. Renyi, A. (1961) Proc. Fourth Berkeley Symp. 1, 547-561
12. (See also A. Renyi, A. (1970), Probability Theory (North-Holland, Amsterdam).)
13. Landsberg, P. T. & Vedral, V. (1998) Phys. Lett. A 247, 211-217.
14. Rajagopal, A. K. & Abe, S. (1999) Phys. Rev. Lett. 83, 1711-1714.
15. Sharma, B. D. & Mittal, D. P. (1975) J. Math. Sci. 10, 28-40.
16. Masi, M. (2005) Phys. Lett. A 338, 217-224.
17. Tsallis, C. (1988) J. Stat. Phys. 52, 479-487.
18. Curado, E. M. F. & Tsallis, C. (1991) J. Phys. A 24, L69-L72, and errata (1991) 24, 3187
19. and Curado, E. M. F. & Tsallis, C. J. Phys. A (1992) 25, 1019.
20. Tsallis, C., Mendes, R. S. & Plastino, A. R. (1998) Physica A 261, 534-554.
21. Lyra, M. L. & Tsallis, C. (1998) Phys. Rev. Lett. 80, 53-56.
22. Borges, E. P., Tsallis, C., Ananos, G. F. J. & Oliveira, P. M. C. (2002) Phys. Rev. Lett. 89, 254103-1-254103-4.
23. Ananos, G. F. J. & Tsallis, C. (2004) Phys. Rev. Lett. 93, 020601-1-20601-4.
24. Mayoral, E. & Robledo, A. (2005) Phys. Rev. E 72, 026209-1-026209-7.
25. Casati, G., Tsallis, C. & Baldovin, F. (2005) Europhys. Lett., in press.
26. Watts, D. J. & Strogatz, S. H. (1998) Nature 393, 440-442.
27. Albert, R. & Barabasi, A.-L. (2002) Rev. Mod. Phys. 74, 47-98.
28. Polya, G. (1962) Mathematical Discovery (Wiley, New York), Vol. 1, p. 88.
29. Plastino, A. R. & Plastino, A. (1995) Physica A 222, 347-354.
30. Tsallis, C. & Bukman, D. J. (1996) Phys. Rev. E 54, R2197-R2200.
31. Tsallis, C. (2005) Milan J. Math. 73, in press.
32. Nivanen, L., Le Mehaute, A. & Wang, Q. A. (2003) Rep. Math. Phys. 52, 437-444.
33. Borges, E. P. (2004) Physica A 340, 95-101.
34. Tsallis, C. (2004) Physica A 340, 1-10.
35. Burlaga, L. F. & Vinas, A. F. (2005) Physica A 356, 375-384.
36. Cohen, E. G. D. (2005) Pramana J. Phys. 64, 635-642.
37. Pais, A. (1982) Subtle Is the Lord: The Science and the Life of Albert Einstein (Oxford Univ. Press, New York).
38. Robledo, A. (2004) Physica A 344, 631-636.
39. Robledo, A. (2005) Mol. Phys., in press.
40. Tsallis, C. (2005) in Complexity, Metastability and Nonextensivity, eds. Beck, C., Benedek, G., Rapisarda, A. & Tsallis, C. (World Scientific, Singapore), pp. 13-32.
41. Soares, D. J. B., Tsallis, C., Mariz, A. M. & Silva, L. R. (2005) Europhys. Lett. 70, 70-76.
42. Thurner, S. & Tsallis, C. (2005) Europhys. Lett. 72, 197-203.
43. Lesche, B. (1982) J. Stat. Phys. 27, 419-422.
44. Abe, S. (2002) Phys. Rev. E 66, 046134-1-046134-6.
45. Lesche, B. (2004) Phys. Rev. E 70, 017102-1-017102-4.
46. Moyano, L. G., Tsallis, C. & Gell-Mann, M. (2005) arXiv. cond-mat/0509229.