publication . Preprint . Conference object . 2007

From Information Geometry to Newtonian Dynamics

Ariel Caticha; Carlo Cafaro; Kevin H. Knuth; Ariel Caticha; Julian L. Center; Adom Giffin; Carlos C. Rodríguez;
Open Access English
  • Published: 04 Oct 2007
Abstract
Comment: Presented at MaxEnt 2007, the 27th International Workshop on Bayesian Inference and Maximum Entropy Methods (July 8-13, 2007, Saratoga Springs, New York, USA)
Subjects
free text keywords: Physics - Classical Physics, General Relativity and Quantum Cosmology, Nonlinear Sciences - Chaotic Dynamics, Physics - Data Analysis, Statistics and Probability, Equations of motion, Phase space, Classical mechanics, Quantum mechanics, Statistical model, Principle of maximum entropy, Physics, Information geometry, Newtonian dynamics, Statistical manifold, Configuration space
Related Organizations

[1] E. T. Jaynes: Phys. Rev. 106, 620 and 108, 171 (1957); E. T. Jaynes: Papers on Probability, Statistics and Statistical Physics, ed. by R. D. Rosenkrantz (Reidel, Dordrecht, 1983).

[2] A. Caticha: Phys. Lett. A244, 13 (1998); Phys. Rev. A57, 1572 (1998); Found. Phys. 30, 227 (2000) (arXiv.org/abs/quant-ph/9810074); “From Objective Amplitudes to Bayesian Probabilities” in Foundations of Probability and Physics-4, ed. by G. Adenier, C. Fuchs, and A. Khrennikov, AIP Conf. Proc. Vol. 889, 62 (2007) (arXiv.org/abs/quant-ph/0610076).

[3] S. Amari and H. Nagaoka, Methods of Information Geometry (Am. Math. Soc./Oxford U. Press, Providence, 2000).

[4] N. N. Cˇencov: Statistical Decision Rules and Optimal Inference, Transl. Math. Monographs, vol. 53, Am. Math. Soc. (Providence, 1981); L. L. Campbell: Proc. Am. Math. Soc. 98, 135 (1986).

[5] 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).

[6] 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).

[7] B. F. Schutz, Geometrical Methods of Mathematical Physics (Cambridge U. Press, 1980).

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

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