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: | EN |
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MDPI AG
2021
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| Subjects: | |
| Online Access: | https://doaj.org/article/38b1a5278ce049d8a10d0be0cf1f4b9f |
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| Summary: | 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. |
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