Kim, E. (2018) Investigating information geometry in classical and quantum systems through information length. Entropy, 20 (8). 574.
Abstract
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
Keywords: | Stochastic processes; Langevin equation; Fokker–Planck equation; information length; Fisher information; relaxation; chaos; attractor; probability density function |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 03 Aug 2018 09:57 |
Last Modified: | 03 Aug 2018 09:57 |
Published Version: | https://doi.org/10.3390/e20080574 |
Status: | Published |
Publisher: | MDPI |
Refereed: | Yes |
Identification Number: | 10.3390/e20080574 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:134128 |