Stationary and dynamical properties of information entropies in nonextensive systems

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

Volumn 77, Issue 3, 2008, Pages

  Hasegawa, Hideo ^a  

^a TOKYO GAKUGEI UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

FISHER INFORMATION MATRIX; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; PROBABILITY DISTRIBUTIONS;

LANGEVIN MODEL; MULTIPLICATIVE NOISE;

ENTROPY;

EID: 41549153747     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.77.031133     Document Type: Article

References (40)

1. B. R. Frieden, Physics from Fisher Information: A Unification (Cambridge University Press, Cambridge, 1998).
2. D. Daems and G. Nicolis, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.59.4000 59, 4000 (1999).
3. B. C. Bag, S. K. Banik, and D. S. Ray, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.026110 64, 026110 (2001).
4. B. C. Bag, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.026122 66, 026122 (2002).
5. D. Osorio-Gonzaler, M. Mayorga, J. Orozco, and L. R. Salazar, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1560933 118, 6989 (2003).
6. B. Q. Ai, X. J. Wang, G. T. Liu, and L. G. Liu, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.022903 67, 022903 (2003).
7. G. Goswami, B. Mukherjee, and B. C. Bag, Chem. Phys. CMPHC2 0301-0104 10.1016/j.chemphys.2004.11.020 312, 47 (2005).
8. S. Amari and H. Nagaoka, Methods of Information Geometry (AMS and Oxford University Press, Oxford, 2000).
9. C. Tsallis, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01016429 52, 479 (1988).
10. C. Tsallis, R. S. Mendes, and A. R. Plastino, Physica A PHYADX 0378-4371 10.1016/S0378-4371(98)00437-3 261, 534 (1998).
11. C. Tsallis, Physica D PDNPDT 0167-2789 10.1016/j.physd.2004.01.006 193, 3 (2004).
12. Lists of many applications of the nonextensive statistics are available at http://tsallis.cat.cbpf.br/biblio.htm
13. A. Plastino and A. R. Plastino, Physica A PHYADX 0378-4371 10.1016/0378-4371(95)00211-1 222, 347 (1995).
14. C. Tsallis and D. J. Bukman, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.54.R2197 54, R2197 (1996).
15. A. Plastino, A. R. Plastino, and H. G. Miller, Physica A PHYADX 0378-4371 10.1016/S0378-4371(96)00386-X 235, 577 (1997).
16. F. Pennini, A. R. Plastino, and A. Plastino, Physica A PHYADX 0378-4371 10.1016/S0378-4371(98)00272-6 258, 446 (1998).
17. L. Borland, F. Pennini, A. R. Plastino, and A. Plastino, Eur. Phys. J. B EPJBFY 1434-6028 10.1007/s100510051006 12, 285 (1999).
18. A. R. Plastino, M. Casas, and A. Plastino, Physica A PHYADX 0378-4371 10.1016/S0378-4371(00)00006-6 280, 289 (2000).
19. S. Abe, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.031101 68, 031101 (2003).
20. J. Naudts, J. Ineq. Pure Appl. Math. 5, 102 (2004). 0862-7940
21. F. Pennini and A. Plastino, Physica A PHYADX 0378-4371 10.1016/j.physa.2003.10.076 334, 132 (2004).
22. M. Portesi, A. Plastino, and F. Pennini, Physica A PHYADX 0378-4371 10.1016/j.physa.2006.01.034 365, 173 (2006).
23. M. Portesi, F. Pennini, and A. Plastino, Physica A PHYADX 0378-4371 10.1016/j.physa.2006.05.024 373, 273 (2007).
24. M. Masi, e-print arXiv:cond-mat/0611300.
25. I. Csiszár, Period. Math. Hung. PMHGAW 0031-5303 10.1007/BF02018661 2, 191 (1972).
26. S. Kullback, Information Theory and Statistics (Wiley, New York, 1975).
27. Hiroshi Hasegawa, Prog. Theor. Phys. Suppl. PTPSEP 0375-9687 162, 183 (2006).
28. A. Ohara, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2007.05.104 370, 184 (2007).
29. B. Lindner, J. García-Ojalvo, A. Neiman, and L. Schimansky-Geilíer, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2003. 10.015 392, 321 (2004).
30. H. Hasegawa, Physica A PHYADX 0378-4371 10.1016/j.physa.2006.08.053 374, 585 (2007).
31. H. Hasegawa, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.041903 67, 041903 (2003).
32. H. Hasegawa, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.75.033001 75, 033001 (2006).
33. H. Hasegawa, Physica A 0378-4371 387, 2697 (2008).
34. H. Sakaguchi, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.70.3247 70, 3247 (2001).
35. C. Anteneodo and C. Tsallis, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1617365 44, 5194 (2003).
36. H. Hasegawa, Physica A PHYADX 0378-4371 10.1016/j.physa.2005.10.004 365, 383 (2006).
37. K. S. Fa, Chem. Phys. CMPHC2 0301-0104 10.1016/S0301-0104(02)00942-4 287, 1 (2003).
38. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
39. H. Hasegawa, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.75.051904 75, 051904 (2007).
40. H. Hasegawa, in Neuronal Network Research Horizons, edited by, M. L. Weiss, (Nova Science, New York, 2007), p. 61.