Sons, Inc. (1972).

[91] V. M. Alekseev and M. V. Yakobson, Phys. Reports 75, 287 (1981).

[92] Y. Pesin, Russan Mathematics Survey 32, 55 (1977).

[93] A. N. Kolmogorov, Three approaches to the quantitative definition of information, Probl. Inf. Transm. (USSR) 1, 4 (1965);

A. N. Kolmogorov, Logical basis for information theory and probability theory, IEEE Trans. Inf. Theory, IT14, 662 (1968);

T. M. Cover and J. A. Thomas, Elements of Information Theory, John Wiley and Sons, Inc. (2006).

[94] F. Benatti, Classical and Quantum Entropies: Dynamics and Information, in Entropy, Princeton University Press (2003);

T. M. Cover and J. A. Thomas, Elements of Information Theory, John Wiley and Sons, Inc. (2006).

[95] Z. Zheng, B. Misra and H. Atmanspacher, Observer-Dependence of Chaos Under Lorentz and Rindler Transformations, Int. J. Theor. Phys. 42, 869 (2003).

[96] N. D. Birrell and P. C. W. Davies, Quantum fields in curved space, Cambridge University Press (1983).

[97] S. E. Rugh, Chaos in the Einstein Equations- Characterization and Importance?, in Deterministic Chaos in General Relativity, NATO ASI Series (1994).

[98] A. Caticha, Entropic Dynamics, Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by R.L. Fry, AIP Conf. Proc. 617, 302 (2002).

[99] A. Caticha, Consistency and Linearity in Quantum Theory, Phys. Lett. A244, 13 (1998); Consistency, Amplitudes and Probabilities in Quantum Theory, Phys. Rev. A57, 1572 (1998); Probability and entropy in quantum theory, Maximum Entropy and Bayesian Methods, ed. by W. Von der Linden et al. (Kluwer, Dordrecht, 1999); Insufficient reason and entropy in quantum theory, Found. Phys. 30, 227 (2000).

[100] A. Caticha, Towards a Statistical Geometrodynamics, Decoherence and Entropy in Complex Systems, ed. by H.-T. Elze (Springer Verlag, 2004); The Information Geometry of Space and Time, presented at the 25th International Work-shop on Maximum Entropy and Bayesian Methods in Science and Engineering (San Jose, California, August 2005), (arXiv.org/abs/gr-qc/0508108).

[101] A. Caticha, Maximum entropy and Bayesian data analysis: Entropic prior distributions, Physical Review E 70, 046127 (2004); A. Caticha, Relative Entropy and Inductive Inference, Bayesian Inference and Maximum Entropy Methods in Sci-ence and Engineering,ed. by G. Erickson and Y. Zhai, AIP Conf. Proc. 707, 75 (2004), (arXiv.org/abs/physics/0311093);A. Caticha and A. Giffin, Updating Probabilities, presented at MaxEnt2006, the 26th International Workshop on Bayesian Inference and Maximum Entropy Methods (Paris, France), (arXiv:physics/0608185).

[102] W. H. Zurek and J. P. Paz, Decoherence, Chaos, and the Second Law, Phys. Rev. Lett. 72, 2508 (1994); Quantum Chaos: a decoherent definition, Physica D83, 300 (1995).

[103] C. M. Caves and R. Schack, Unpredictability, Information, and Chaos, Complexity 3, 46 (1997).

[104] A. M. Lyapunov, Stability of Motion, Academic Press (1966); S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer (2003).

[105] F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer (1990).

[106] J. P. Eckmann and D. Ruelle, Ergodic theory of chaos and strange attractors, Rev. Mod. Phys. vol. 57, 617-656 (1985).

[107] T. Bhattacharya, S. Habib and K. Jacobs, Continuous Quantum Measurement and the Emergence of Classical Chaos, Phys. Rev. Lett. 85, 4852 (2000); G. Casati and B. Chirikov, The legacy of chaos in quantum mechanics, in Quantum Chaos, Cambridge University Press (1995).

[108] V. Latora and M. Baranger, Kolmogorov-Sinai Entropy Rate versus Physical Entropy, Phys. Rev. Lett. 82, 520 (1999).

[109] M. Toda and K. Ikeda, Quantal Lyapunov Exponent, Phys. Lett. A124, 165 (1987).

[110] C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation, Freeman and Company- San Francisco (1973).

[111] C. Chicone and B. Mashhoon, The generalized Jacobi equation, Class. Quantum Grav. 19, 4231-4248 (2002).

[112] K. Arwini and C. T. J. Dodson, Information geometric neighbourhoods of randomness and geometry of the Mckay bivariate gamma 3-manifold, Indian Journal of Statistics 66, 211-231 (2004).

[113] B. Efron, Defining the curvature of a statistical problem, Annals of Statistics 3, 1189 (1975).

[114] C. C. Rodriguez, Are we cruising a hypothesis space?, in Maximum Entropy and Bayesian Methods, ed. by W. Von der Linden, V. Dose, R. Fischer and R. Press (Kluwer, Dordrecht, 1999).

[115] A. Caticha, Relative Entropy and Inductive Inference, Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by G. Erickson and Y. Zhai, AIP Conf. Proc. 707, 75 (2004); A. Caticha and A. Giffin, Updating Probabilities, AIP Conf. Proc. 872, 31-42 (2006); A. Caticha and R. Preuss, Maximum entropy and Bayesian data analysis: Entropic prior distributions, Phys. Rev. E70, 046127 (2004).

[116] A. Caticha, Entropic Dynamics, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by R. L. Fry, AIP Conf. Proc. 617, 302 (2002). (arXiv.org/abs/gr-qc/0109068).

[117] A. Caticha, Towards a Statistical Geometrodynamics, in Decoherence and Entropy in Complex Systems ed. by H.-T. Elze (Springer Verlag, 2004) (arXiv.org/abs/gr-qc/0301061); The Information geometry of Space and Time, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by K. Knuth, A. Abbas, R. Morris, and J. Castle, AIP Conf. Proc. 803, 355 (2006) (arXiv.org/abs/cond-mat/0508108).

[118] C. Lanczos, The Variational Principles of Mechanics (Dover, New York, 1986).

[119] C. Cafaro, S. A. Ali and A. Giffin, An Application of Reversible Entropic Dynamics on Curved Statistical Manifolds,

in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by Ali Mohammad-Djafari, AIP Conf. Proc. 872, 243-251 (2006); arXiv: physics/0702011 (2007).

[120] C. Cafaro, Information-Geometric Indicators of Chaos in Gaussian Models on Statistical Manifolds of Negative Ricci Curvature, arXiv: nlin.CD/0702029, (2007); C. Cafaro, Information Geometry and Chaos on Negatively Curved Statistical Manifolds, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by K. Knuth et. al, AIP Conf. Proc. (2007).

[121] C. Cafaro and S. A. Ali, Jacobi Fields on Statistical Manifolds of Negative Curvature, Physica D234, 70-80 (2007); arXiv: nlin.CD/0702027 (2007).

[122] A. Caticha, Entropic Dynamics, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by R.L. Fry, AIP Conf. Proc. 617, 302 (2002).

[123] A. Caticha, Relative Entropy and Inductive Inference, Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by G. Erickson and Y. Zhai, AIP Conf. Proc. 707, 75 (2004); A. Caticha and A. Giffin, Updating Probabilities, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by Ali Mohammad-Djafari, AIP Conf. Proc. 872, 31-42 (2006); A. Caticha and R. Preuss, Maximum entropy and Bayesian data analysis: Entropic prior distributions, Phys. Rev. E70, 046127 (2004).

[124] G. Casati and B. Chirikov, Quantum Chaos, Cambridge University Press (1995).

[125] F. De Felice and J. S. Clarke, Relativity on Curved Manifolds, Cambridge University Press (1990); M. P. do Carmo, Riemannian Geometry, Birkhauser, Boston, 1992.

[126] N. S. Krylov, Works on the Foundations of Statistical Physics, Princeton University Press, Princeton, 1979.

[127] M. Pellicott, Exponential Mixing for the Geodesic Flow on Hyperbolic Three-Manifolds, Journal of Statistical Physics 67, 667 (1992).

[128] J. Jost, Compact Riemann Surfaces: An Introduction to Contemporary Mathematics, Springer-Verlag (1997).

[129] C. G. J. Jacobi, Vorlesungen uber Dynamik, Reimer, Berlin (1866).

[130] M. Biesiada, The Power of the Maupertuis-Jacobi Principle- Dreams and Reality, Chaos, Solitons & Fractals 5, 869 (1994).

[131] M. Biesiada, Searching for an invariant description of chaos in general relativity, Class. Quantum Grav. 12, 715 (1995).

[132] J. M. Lee, Riemannian Manifolds: An Introduction to Curvature, Springer Verlag (1997).

[133] M. P. do Carmo, Riemannian Geometry, Birkhauser, Boston, 1992.

[134] D. E. Hodgkinson, A modified equation of geodesic deviation, Gen. Rel. Grav. 3, 351 (1972).

[135] D. P. Feldman and J. P. Crutchfield, Measures of complexity: Why?, Phys. Lett. A238, 244-252 (1998); A. Manning, Topological entropy for geodesic flows, Annals of Mathematics 110, 567-573 (1979).

[136] S. Stenholm and K. Suominen, Quantum Approach to Informatics, Wiley-Interscience (2005).

[137] R. Schack and C. M. Caves, Hypersensitivity to perturbation: An information-theoretical characterization of classical and quantum chaos, in Quantum Communication, Computing, and Measurement, edited by O. Hirota, A. S. Holevo, and C. M. Caves, 317-330 (1997).

[138] F. Benatti, Deterministic Chaos in Infinite Quantum Systems, Springer-Verlag Berlin (1993); F. Benatti, Classical and Quantum Entropies: Dynamics and Information, in Entropy edited by A. Greven et. al., Princeton Series in Applied Mathematics (2003).

[139] R. Alicki and M. Fannes, Defining Quantum Dynamical Entropy, Lett. Math. Phys. 32, 75-82 (1994); R. Alicki and M. Fannes, Quantum Dynamical Systems, Oxford University Press (2001).

[140] A. Connes et. al., Dynamical Entropy of C ∗ Algebras and von Neumann Algebras, Commun. Math. Phys. 112, 691-719(1987).

[141] W. H. Zurek, Phys. Today 44. No 10, 36 (1991); 46, No. 12, 81 (1993); Prog. Theor. Phys. 89, 281 (1993).

[142] M. Biesiada and S. E. Rugh, Maupertuis principle, Wheeler’s superspace and an invariant criterion for local stability in general relativity, arXiv: gr-qc/9408030 (1994).

[143] J. Stewart, Advanced General Relativity, Cambridge University Press (1991).