The effect of microscopic correlations on the information geometric complexity of Gaussian statistical models

Physica A: Statistical Mechanics and its Applications

Volumn 389, Issue 16, 2010, Pages 3117-3127

  Ali, S A ^a   Cafaro, C ^b   Kim, D H ^c,d   Mancini, S ^b  

^a STATE UNIVERSITY OF NEW YORK   (United States)

^b UNIVERSITY OF CAMERINO   (Italy)

^c Ewha Womans University   (South Korea)

^d Sogang University   (South Korea)

Author keywords

Chaos; Complexity; Entropy; Probability theory; Riemannian geometry

Indexed keywords

CHAOS THEORY; DYNAMICAL SYSTEMS; ENTROPY; GAUSSIAN DISTRIBUTION;

ANALYTICAL COMPUTATIONS; COMPLEXITY; CORRELATION COEFFICIENT; GAUSSIAN STATISTICAL MODELS; MICROSCOPIC CORRELATIONS; PROBABILITY THEORY; RIEMANNIAN GEOMETRY; STATISTICAL-DYNAMICAL;

GEOMETRY;

EID: 77953128348     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2010.03.028     Document Type: Article

References (30)

1. Gell-Mann M. What is complexity. Complexity 1 (1995) 1
2. Caticha A. Entropic dynamics. In: Fry R.L. (Ed). Bayesian Inference and Maximum Entropy Methods in Science and Engineering. AIP Conf. Proc. vol. 617 (2002) 302
3. C. Cafaro, The information geometry of chaos, Ph.D. Thesis, SUNY at Albany, NY, USA, 2008.
4. Cafaro C. Works on an information geometrodynamical approach to chaos. Chaos Solitons Fractals 41 (2009) 886
5. Caticha A., and Preuss R. Maximum entropy and Bayesian data analysis: entropic prior distributions. Phys. Rev. E 70 (2004) 046127
6. A. Giffin, Maximum entropy: the universal method for inference, Ph.D. Thesis, SUNY at Albany, NY, USA, 2008.
7. Amari S., and Nagaoka H. Methods of Information Geometry (2000), American Mathematical Society, Oxford University Press
8. Casetti L., Clementi C., and Pettini M. Riemannian theory of Hamiltonian chaos and Lyapunov exponents. Phys. Rev. E 54 (1996) 5969
9. Di Bari M., and Cipriani P. Geometry and chaos on Riemann and Finsler manifolds. Planet. Space Sci. 46 (1998) 1543
10. Jacobi C.G.J. Vorlesungen Uber Dynamik (1866), Reimer, Berlin
11. Kawabe T. Indicator of chaos based on the Riemannian geometric approach. Phys. Rev. E 71 (2005) 017201
12. Kawabe T. Chaos based on Riemannian geometric approach to Abelian-Higgs dynamical system. Phys. Rev. E 67 (2003) 016201
13. Lebowitz J.L. Microscopic dynamics and macroscopic laws. Ann. New York Acad. Sci. 373 (1981) 220
14. Lebowitz J.L. Macroscopic laws, microscopic dynamics, time's arrow and Boltzmann's entropy. Physica A 194 (1993) 1
15. Lebowitz J.L. Microscopic origins of irreversible macroscopic behavior. Physica A 263 (1999) 516
16. Toffoli T. How cheap can mechanics' first principles be?. In: Zurek W.H. (Ed). Complexity, Entropy and the Physics of Information (1990), Addison-Wesley 301
17. Shibata T., et al. Noiseless collective motion out of noisy chaos. Phys. Rev. Lett. 82 (1999) 4424
18. Tribus M. Rational Descriptions, Decisions and Designs (1969), Pergamon Press
19. Caticha A. Relative entropy and inductive inference. In: Erickson G., and Zhai Y. (Eds). Bayesian Inference and Maximum Entropy Methods in Science and Engineering. AIP Conf. Proc. vol. 707 (2004) 75
20. Caticha A., and Giffin A. Updating probabilities. In: Mohammad-Djafari A. (Ed). Bayesian Inference and Maximum Entropy Methods in Science and Engineering. AIP Conf. Proc. vol. 872 (2006) 31
21. Jaynes E.T. Information theory and statistical mechanics, I. Phys. Rev. 106 (1957) 620 Information theory and statistical mechanics, II, Phys. Rev. 108 (1957) 171
22. Cafaro C. Information-geometric indicators of chaos in Gaussian models on statistical manifolds of negative Ricci curvature. Int. J. Theor. Phys. 47 (2008) 2924
23. Rozanov Y.A. Probability Theory: A Concise Course (1977), Dover Publications, New York
24. De Felice F., and Clarke J.S. Relativity on Curved Manifolds (1990), Cambridge University Press
25. Cafaro C. Information geometry, inference methods and chaotic energy levels statistics. Modern Phys. Lett. B 22 (2008) 1879
26. Hartnett D.H. Introduction to Statistical Methods (1975), Addison-Wesley
27. M.A. Nielsen, Quantum information science as an approach to complex quantum systems, 2002. arXiv:quant-ph/0208078.
28. Cafaro C., and Ali S.A. Can chaotic quantum energy levels statistics be characterized using information geometry and inference methods?. Physica A 387 (2008) 6876
29. Prosen T. Chaos and complexity of quantum motion. J. Phys. A 40 (2007) 7881
30. Benenti G., and Casati G. How complex is quantum motion?. Phys. Rev. E 79 (2009) 025201