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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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/11/1393 |
| _version_ | 1797510424550178816 |
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| author | Eun-jin Kim |
| author_facet | Eun-jin Kim |
| author_sort | Eun-jin Kim |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T05:31:18Z |
| format | Article |
| id | doaj.art-38b1a5278ce049d8a10d0be0cf1f4b9f |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T05:31:18Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-38b1a5278ce049d8a10d0be0cf1f4b9f2023-11-22T23:14:21ZengMDPI AGEntropy1099-43002021-10-012311139310.3390/e23111393Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex SystemsEun-jin Kim0Center for Fluid and Complex Systems, Coventry University, Priory St, Coventry CV1 5FB, UKInformation 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.https://www.mdpi.com/1099-4300/23/11/1393information geometryentropyinformation rateinformation lengthfluctuationsLangevin equations |
| spellingShingle | Eun-jin Kim Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems Entropy information geometry entropy information rate information length fluctuations Langevin equations |
| title | 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_short | Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems |
| title_sort | information geometry fluctuations non equilibrium thermodynamics and geodesics in complex systems |
| topic | information geometry entropy information rate information length fluctuations Langevin equations |
| url | https://www.mdpi.com/1099-4300/23/11/1393 |
| work_keys_str_mv | AT eunjinkim informationgeometryfluctuationsnonequilibriumthermodynamicsandgeodesicsincomplexsystems |