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

Center for Fluid and Complex Systems, Coventry University, Priory St, Coventry CV1 5FB, UK
Academic Editor: Miguel Rubi
Received: 29 September 2021 / Revised: 15 October 2021 / Accepted: 19 October 2021 / Published: 24 October 2021
(This article belongs to the Special Issue Review Papers for Entropy)
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 dynamic 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 Γ=dLdt 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, L 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. View Full-Text
Keywords: information geometry; entropy; information rate; information length; fluctuations; Langevin equations; Fokker-planck equation; time-dependent probability density functions; self-organization information geometry; entropy; information rate; information length; fluctuations; Langevin equations; Fokker-planck equation; time-dependent probability density functions; self-organization
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MDPI and ACS Style

Kim, E.-j. Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems. Entropy 2021, 23, 1393. https://0-doi-org.brum.beds.ac.uk/10.3390/e23111393

AMA Style

Kim E-j. Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems. Entropy. 2021; 23(11):1393. https://0-doi-org.brum.beds.ac.uk/10.3390/e23111393

Chicago/Turabian Style

Kim, Eun-jin. 2021. "Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems" Entropy 23, no. 11: 1393. https://0-doi-org.brum.beds.ac.uk/10.3390/e23111393

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