Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems

Information theory provides an interdisciplinary method to understand important phenomena in many research fields ranging from astrophysical and laboratory fluids/plasmas to biological systems. In particular, information geometric theory enables us to envision the evolution of non-equilibrium proces...

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Autor principal:	Eun-jin Kim
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	information geometry entropy information rate information length fluctuations Langevin equations Science Q Astrophysics QB460-466 Physics QC1-999
Acceso en línea:	https://doaj.org/article/38b1a5278ce049d8a10d0be0cf1f4b9f
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spelling	oai:doaj.org-article:38b1a5278ce049d8a10d0be0cf1f4b9f2021-11-25T17:29:16ZInformation Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems10.3390/e231113931099-4300https://doaj.org/article/38b1a5278ce049d8a10d0be0cf1f4b9f2021-10-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1393https://doaj.org/toc/1099-4300Information theory provides an interdisciplinary method to understand important phenomena in many research fields ranging from astrophysical and laboratory fluids/plasmas to biological systems. In particular, information geometric theory enables us to envision the evolution of non-equilibrium processes in terms of a (dimensionless) distance by quantifying how information unfolds over time as a probability density function (PDF) evolves in time. Here, we discuss some recent developments in information geometric theory focusing on time-dependent <i>dynamic</i> aspects of non-equilibrium processes (e.g., time-varying mean value, time-varying variance, or temperature, etc.) and their thermodynamic and physical/biological implications. We compare different distances between two given PDFs and highlight the importance of a path-dependent distance for a time-dependent PDF. We then discuss the role of the information rate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Γ</mo><mo>=</mo><mfrac><mrow><mi>d</mi><mi mathvariant="script">L</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow></semantics></math></inline-formula> and relative entropy in non-equilibrium thermodynamic relations (entropy production rate, heat flux, dissipated work, non-equilibrium free energy, etc.), and various inequalities among them. Here, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">L</mi></semantics></math></inline-formula> is the information length representing the total number of statistically distinguishable states a PDF evolves through over time. We explore the implications of a geodesic solution in information geometry for self-organization and control.Eun-jin KimMDPI AGarticleinformation geometryentropyinformation rateinformation lengthfluctuationsLangevin equationsScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1393, p 1393 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	information geometry entropy information rate information length fluctuations Langevin equations Science Q Astrophysics QB460-466 Physics QC1-999
spellingShingle	information geometry entropy information rate information length fluctuations Langevin equations Science Q Astrophysics QB460-466 Physics QC1-999 Eun-jin Kim Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems
description	Information theory provides an interdisciplinary method to understand important phenomena in many research fields ranging from astrophysical and laboratory fluids/plasmas to biological systems. In particular, information geometric theory enables us to envision the evolution of non-equilibrium processes in terms of a (dimensionless) distance by quantifying how information unfolds over time as a probability density function (PDF) evolves in time. Here, we discuss some recent developments in information geometric theory focusing on time-dependent <i>dynamic</i> aspects of non-equilibrium processes (e.g., time-varying mean value, time-varying variance, or temperature, etc.) and their thermodynamic and physical/biological implications. We compare different distances between two given PDFs and highlight the importance of a path-dependent distance for a time-dependent PDF. We then discuss the role of the information rate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Γ</mo><mo>=</mo><mfrac><mrow><mi>d</mi><mi mathvariant="script">L</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow></semantics></math></inline-formula> and relative entropy in non-equilibrium thermodynamic relations (entropy production rate, heat flux, dissipated work, non-equilibrium free energy, etc.), and various inequalities among them. Here, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">L</mi></semantics></math></inline-formula> is the information length representing the total number of statistically distinguishable states a PDF evolves through over time. We explore the implications of a geodesic solution in information geometry for self-organization and control.
format	article
author	Eun-jin Kim
author_facet	Eun-jin Kim
author_sort	Eun-jin Kim
title	Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems
title_short	Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems
title_full	Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems
title_fullStr	Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems
title_full_unstemmed	Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems
title_sort	information geometry, fluctuations, non-equilibrium thermodynamics, and geodesics in complex systems
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/38b1a5278ce049d8a10d0be0cf1f4b9f
work_keys_str_mv	AT eunjinkim informationgeometryfluctuationsnonequilibriumthermodynamicsandgeodesicsincomplexsystems
_version_	1718412277436121088

Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems

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