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Investigating Information Geometry in Classical and Quantum Systems through Information Length

School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH, UK
Entropy 2018, 20(8), 574; https://doi.org/10.3390/e20080574
Received: 19 July 2018 / Revised: 1 August 2018 / Accepted: 1 August 2018 / Published: 3 August 2018
(This article belongs to the Special Issue Entropy: From Physics to Information Sciences and Geometry)
Stochastic processes are ubiquitous in nature and laboratories, and play a major role across traditional disciplinary boundaries. These stochastic processes are described by different variables and are thus very system-specific. In order to elucidate underlying principles governing different phenomena, it is extremely valuable to utilise a mathematical tool that is not specific to a particular system. We provide such a tool based on information geometry by quantifying the similarity and disparity between Probability Density Functions (PDFs) by a metric such that the distance between two PDFs increases with the disparity between them. Specifically, we invoke the information length L(t) to quantify information change associated with a time-dependent PDF that depends on time. L(t) is uniquely defined as a function of time for a given initial condition. We demonstrate the utility of L(t) in understanding information change and attractor structure in classical and quantum systems. View Full-Text
Keywords: stochastic processes; Langevin equation; Fokker–Planck equation; information length; Fisher information; relaxation; chaos; attractor; probability density function stochastic processes; Langevin equation; Fokker–Planck equation; information length; Fisher information; relaxation; chaos; attractor; probability density function
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MDPI and ACS Style

Kim, E.-j. Investigating Information Geometry in Classical and Quantum Systems through Information Length. Entropy 2018, 20, 574. https://doi.org/10.3390/e20080574

AMA Style

Kim E-j. Investigating Information Geometry in Classical and Quantum Systems through Information Length. Entropy. 2018; 20(8):574. https://doi.org/10.3390/e20080574

Chicago/Turabian Style

Kim, Eun-jin. 2018. "Investigating Information Geometry in Classical and Quantum Systems through Information Length" Entropy 20, no. 8: 574. https://doi.org/10.3390/e20080574

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