The world according to Rényi: Thermodynamics of multifractal systems

Annals of Physics

Volumn 312, Issue 1, 2004, Pages 17-59

  Jizba, Petr ^a   Arimitsu, Toshihico ^a  

^a UNIVERSITY OF TSUKUBA   (Japan)

Author keywords

MaxEnt; Multifractals; R nyi's information entropy; Tsallis Havrda Charvat entropy

Indexed keywords

EID: 3142672769     PISSN: 00034916     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aop.2004.01.002     Document Type: Article

References (66)

1. Havrda J.H. Charvat F. Kybernatica 3 1967 30
2. Tsallis C. J. Stat. Phys. 52 1988 479
3. Tsallis C. Braz. J. Phys. 29 1999 1
4. Rényi A. Probability Theory 1970 North-Holland Amsterdam
5. Rényi A. (Ed.). Selected Papers of Alfred Rényi vol. 2 1976 Akadémia Kiado Budapest
6. Frisch U. Parisi G. Ghil M. Benzi R. Parisi G. (Eds.). Turbulence and Predictibility in Geophysical Fluid Dynamics and Climate Dynamics 1985 North-Holland New York
7. Arimitsu T. Arimitsu N. Physica A 295 2001 177
8. T. Arimitsu, N. Arimitsu, J. Phys. A: Math. Gen. 33 (2000) L235 [CORRIGENDUM: 34 (2001) 673]
9. Arimitsu T. Arimitsu N. Physica A 305 2002 218
10. Arimitsu T. Arimitsu N. J. Phys.: Condens. Matter 14 2002 2237
11. T. Arimitsu, N. Arimitsu, Analysis of Accelerations in Turbulence based on Generalized Statistics (2002) [cond-mat/0203240]
12. Aharony A. Pynn R. Riste T. (Eds.). Time-Dependent Effects in Disordered Materials 1987 Plenum Press New York
13. Amitrano C. Coniglio A. di Liberto F. Phys. Rev. Lett. 57 1986 1016
14. Yu Z.-G. Anh V. Lau K.-S. Phys. Rev. E 64 2001 031903
15. Anh V.V. Tieng Q.M. Tse Y.K. Int. Trans. Op. Res. 7 2000 349
16. Mineev-Weinstein M. Wiegmann P.B. Zabrodin A. Phys. Rev. Lett. 84 2000 5106
17. T. Arimitsu, P. Jizba, M. Sakellariadou, work in progress
18. Aczél J. Lectures on Functional Equations and their Applications 1966 Academic Press New York
19. Balian R. (Ed.). From Microphysics to Macrophysics, Methods and Applications of Statistical Physics vol.1 1991 Springer-Verlag Heidelberg
20. Hartley R.V. Bell Syst. Techn. J. 7 1928 535
21. Kolmogorov A. Atti della R. Accademia Nazionale dei Lincei 12 1930 388
22. Nagumo M. Jpn. J. Math. 7 1930 71
23. Aczél J. Bull. Amer. Math. Soc. 54 1948 392
24. Hardy G.H. Littlewood J.E. Pólya G. Inequalities 1952 Cambridge University Press Cambridge
25. Shannon C.E. Weaver W. The Mathematical Theory of Communication 1949 University of Illinois Press New York
26. Feinstein A. Foundations of Information Theory 1958 McGraw-Hill New York
27. Khinchin A.I. Mathematical Foundations of Information Theory 1957 Dover Publications Inc New York
28. T.W. Chaudy, J.B. McLeod, Edinburgh Mathematical Notes 43 (1960) 7; for H. Tverberg's, P.M. Lee's or D.G. Kendall's axiomatics of Shannon's entropy see e.g., S. Guias, Information Theory with Applications [25]
29. Daróczy Z. Acta Math. Acad. Sci. Hungaricae 15 1964 203
30. see e.g., S. Guias, Information Theory with Applications. McGraw-Hill, New York, 1977
31. Marshall A.W. Olkin I. J. Math. Anal. Appl. 8 1964 503
32. Abe S. Phys. Lett. A 271 2000 74
33. http://tsallis.cat.cbpf.br/biblio.htm
34. Loève M. (Ed.). Probability Theory vol. 1 1977 Springer-Verlag Berlin
35. Schrödinger E. Statistical Thermodynamics 1989 Dover Publications Inc New York
36. Jaynes E.T. Ford K.W. (Ed.). Information Theory and Statistical Mechanics vol. 3 1963 W.A. Benjamin Inc New York
37. Jaynes E.T. Papers on Probability and Statistics and Statistical Physics 1983 D. Reidel Publishing Company Boston
38. Szilard L. Z. Phys. 53 1929 840
39. Brillouin L. J. Appl. Phys. 22 1951 334
40. Mandelbrot B.B. Fractal-Form, Chance and Dimension 1977 Freeman San francisco
41. Feder J. Fractals 1988 Plenum Press New York
42. Halsey T.C. Jensen M.H. Kadanoff L.P. Procaccia I. Schraiman B.I. Phys. Rev. A 33 1986 1141
43. Morse P.M. Feshbach H. Methods of Theoretical Physics vol. 1 1953 McGraw-Hill New York
44. Hentschel H.G.E. Procaccia I. Physica D 8 1983 435
45. Ruelle D. Chaotic Evolution and Strange Attractors 1989 Cambridge University Press Cambridge
46. Widder D.V. The Laplace Transform 1946 Princeton University Press Princeton
47. Billingsley P. Ergodic Theory and Information 1965 Wiley New York
48. Caratheodory C. Math. Ann. 67 1909 355
49. Buchdahl H.A. Am. J. Phys. 17 1949 212
50. Khinchin A.I. Mathematical Foundations of Statistical Mechanics 1949 Dover Publications Inc New York
51. Jizba P. Tututi E.S. Phys. Rev. D 60 1999 105013
52. P. Jizba, E.S. Tututi, in: U. Heinz (Eds.), 5th International Workshop on Thermal Field Theories and Their Applications 10-14 August 1998, Regensburg, Germany, hep-th/9809110
53. P. Jizba, Equilibrium and Nonequilibrium Quantum Field Theory, Ph.D. thesis, University of Cambridge, hep-th/9910259
54. Ball R.C. Blumenfeld R. Phys. Rev. A 44 1991 828
55. Mandelbrot B.B. Evertsz C.J.G. Nature 348 1990 143
56. Edgar G.A. Integral, Probability, and Fractal Measures 1997 Springer-Verlag New York
57. Barnsley M.F. Fractals Everywhere 1988 Academic Press Boston
58. Kullback S. Information Theory and Statistics 1959 Wiley New York
59. Kibble T.W. J. Phys. A 9 1976 1387
60. Zurek W.H. Phys. Rept. 276 1996 177
61. Hagedorn R. Nuovo Cim. Suppl. 3 1965 147
62. Turok N. Physica A 158 1989 516
63. P. Jizba, T. Arimitsu, see the Proceedings of International Symposium on Nonequilibrium and Nonlinear Dynamics, in: Z. Li, K. Wu, X. Wu, E. Zhao, F. Sakata (Eds.), Nuclear and Other Finite Systems-AIP Conference Proceedings, vol. 597, 1, (2001) p. 341
64. Feynman R.P. Gorter C.J. Progress in Low Temperature Physics vol. 1 1955 17 North-Holland Amsterdam
65. Davis S.L. Hendry P.C. McClintock P.V.E. Physica B 280 2000 43
66. Kapur J.M. Math. Semin. Delhi 4 1967 78