Information-geometric indicators of Chaos in Gaussian models on statistical manifolds of negative ricci curvature

International Journal of Theoretical Physics

Volumn 47, Issue 11, 2008, Pages 2924-2933

  Cafaro, Carlo ^a  

^a STATE UNIVERSITY OF NEW YORK   (United States)

Author keywords

Chaos; Entropy; Inductive inference; Information geometry; Nonlinear dynamics; Statistical manifolds

Indexed keywords

EID: 53549132247     PISSN: 00207748     EISSN: 15729575     Source Type: Journal    
DOI: 10.1007/s10773-008-9726-x     Document Type: Article

References (34)

1. Caticha, A.: Entropic dynamics. In: Fry, R.L. (ed.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering. AIP Conf. Proc., vol. 617, p. 302 (2002)
2. Caticha, A.: Relative entropy and inductive inference. In: Erickson, G., Zhai, Y. (eds.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering. AIP Conf. Proc., vol. 707, p. 75 (2004)
3. Caticha, A., Giffin, A.: Updating probabilities. In: Mohammad-Djafari, A. (ed.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering. AIP Conf. Proc., vol. 872, pp. 31-42 (2006)
4. A. Caticha R. Preuss 2004 Maximum entropy and Bayesian data analysis: entropic prior distributions Phys. Rev. E 70 046127
5. Amari, S., Nagaoka, H.: Methods of Information Geometry. American Mathematical Society, Providence (2000)
6. E.T. Jaynes 1957 Information theory and statistical mechanics I Phys. Rev. 106 620
7. E.T. Jaynes 1957 Information theory and statistical mechanics II Phys. Rev. 108 171
8. A. Caticha 1998 Consistency and linearity in quantum theory Phys. Lett. A 244 13
9. A. Caticha 1998 Consistency, amplitudes and probabilities in quantum theory Phys. Rev. A 57 1572
10. R.A. Fisher 1925 Theory of statistical estimation Proc. Camb. Philos. Soc. 122 700
11. C.R. Rao 1945 Information and accuracy attainable in the estimation of statistical parameters Bull. Calcutta Math. Soc. 37 81
12. C.M. Caves R. Schack 1997 Unpredictability, information, and chaos Complexity 3 46 57
13. A.J. Scott T.A. Brun C.M. Caves R. Schack 2006 Hypersensitivity and chaos signatures in the quantum baker's map J. Phys. A 39 13405
14. L. Casetti C. Clementi M. Pettini 1996 Riemannian theory of Hamiltonian chaos and Lyapunov exponents Phys. Rev. E 54 5969 5984
15. M. Di Bari P. Cipriani 1998 Geometry and chaos on Riemann and Finsler manifolds Planet. Space Sci. 46 1543
16. T. Kawabe 2005 Indicator of chaos based on the Riemannian geometric approach Phys. Rev. E 71 017201
17. W.H. Zurek J.P. Paz 1994 Decoherence, chaos, and the second law Phys. Rev. Lett. 72 2508
18. W.H. Zurek J.P. Paz 1995 Quantum chaos: a decoherent definition Physica D 83 300
19. J.P. Eckmann D. Ruelle 1985 Ergodic theory of chaos and strange attractors Rev. Mod. Phys. 57 617 656
20. Jaynes, E.T.: Probability Theory: The Logic of Science. Cambridge University Press, Cambridge (2003)
21. Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. Freeman, New York (1973)
22. Cafaro, C., Ali, S.A., Giffin, A.: An application of reversible entropic dynamics on curved statistical manifolds. In: Mohammad-Djafari, A. (ed.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering. AIP Conf. Proc., vol. 872, pp. 243-251 (2006)
23. C. Cafaro S.A. Ali 2007 Jacobi fields on statistical manifolds of negative curvature Physica D 234 70 80 arXiv: nlin.CD/0702027
24. Cafaro, C.: Information geometry and chaos on negatively curved statistical manifolds. In: Knuth, K. et al. (eds.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering. AIP Conf. Proc., vol. 954, p. 165 (2007)
25. Arnold, V.I.: Mathematical Methods of Classical Physics. Springer, New York (1989)
26. De Felice, F., Clarke, J.S.: Relativity on Curved Manifolds. Cambridge University Press, Cambridge (1990)
27. Lee, J.M.: Riemannian Manifolds: An Introduction to Curvature. Springer, New York (1997)
28. Benatti, F.: Classical and quantum entropies: dynamics and information. In: Greven, A., Keller, G., Warnecke, G. (eds.) Entropy. Princeton University Press, Princeton (2003)
29. W.H. Zurek 1993 Preferred states, predictability, classicality and environment-induced decoherence Prog. Theor. Phys. 89 281
30. do Carmo, M.P.: Riemannian Geometry. Birkhäuser, Boston (1992)
31. Ohanian, H.C., Ruffini, R.: Gravitation and Spacetime. Norton, New York (1994)
32. C. Chicone B. Mashhoon 2002 The generalized Jacobi equation Class. Quantum Gravity 19 4231 4248
33. D.P. Feldman J.P. Crutchfield 1998 Measures of complexity: Why? Phys. Lett. A 238 244 252
34. A. Manning 1979 Topological entropy for geodesic flows Ann. Math. 110 567 573