Information geometry and chaos on negatively curved statistical manifolds

Carlo Cafaro

doi:10.1063/1.2821260

Information geometry and chaos on negatively curved statistical manifolds

Carlo Cafaro

Nanoscale Science and Engineering

University at Albany

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

8 Scopus citations

Abstract

A novel information-geometric approach to chaotic dynamics on curved statistical manifolds based on Entropic Dynamics (ED) is suggested. Furthermore, an information-geometric analogue of the Zurek-Paz quantum chaos criterion is proposed. It is shown that the hyperbolicity of a non-maximally symmetric 6N-dimensional statistical manifold M_s underlying an ED Gaussian model describing an arbitrary system of 3N non-interacting degrees of freedom leads to linear information-geometric entropy growth and to exponential divergence of the Jacobi vector field intensity, quantum and classical features of chaos respectively.

Original language	English
Title of host publication	Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007
Pages	175-184
Number of pages	10
DOIs	https://doi.org/10.1063/1.2821260
State	Published - 2007
Event	27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007 - Saratoga Springs, NY, United States Duration: Jul 8 2007 → Jul 13 2007

Publication series

Name	AIP Conference Proceedings
Volume	954

Conference

Conference	27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007
Country/Territory	United States
City	Saratoga Springs, NY
Period	07/8/07 → 07/13/07

Access to Document

10.1063/1.2821260

Cite this

Cafaro, C. (2007). Information geometry and chaos on negatively curved statistical manifolds. In Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007 (pp. 175-184). (AIP Conference Proceedings; Vol. 954). https://doi.org/10.1063/1.2821260

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title = "Information geometry and chaos on negatively curved statistical manifolds",

abstract = "A novel information-geometric approach to chaotic dynamics on curved statistical manifolds based on Entropic Dynamics (ED) is suggested. Furthermore, an information-geometric analogue of the Zurek-Paz quantum chaos criterion is proposed. It is shown that the hyperbolicity of a non-maximally symmetric 6N-dimensional statistical manifold Ms underlying an ED Gaussian model describing an arbitrary system of 3N non-interacting degrees of freedom leads to linear information-geometric entropy growth and to exponential divergence of the Jacobi vector field intensity, quantum and classical features of chaos respectively.",

author = "Carlo Cafaro",

year = "2007",

doi = "10.1063/1.2821260",

language = "English",

isbn = "9780735404687",

series = "AIP Conference Proceedings",

pages = "175--184",

booktitle = "Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007",

note = "27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007 ; Conference date: 08-07-2007 Through 13-07-2007",

}

Cafaro, C 2007, Information geometry and chaos on negatively curved statistical manifolds. in Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007. AIP Conference Proceedings, vol. 954, pp. 175-184, 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007, Saratoga Springs, NY, United States, 07/8/07. https://doi.org/10.1063/1.2821260

Information geometry and chaos on negatively curved statistical manifolds. / Cafaro, Carlo.
Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007. 2007. p. 175-184 (AIP Conference Proceedings; Vol. 954).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - A novel information-geometric approach to chaotic dynamics on curved statistical manifolds based on Entropic Dynamics (ED) is suggested. Furthermore, an information-geometric analogue of the Zurek-Paz quantum chaos criterion is proposed. It is shown that the hyperbolicity of a non-maximally symmetric 6N-dimensional statistical manifold Ms underlying an ED Gaussian model describing an arbitrary system of 3N non-interacting degrees of freedom leads to linear information-geometric entropy growth and to exponential divergence of the Jacobi vector field intensity, quantum and classical features of chaos respectively.

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BT - Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007

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Y2 - 8 July 2007 through 13 July 2007

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Information geometry and chaos on negatively curved statistical manifolds

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