Abstract
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 = dL dt 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.
Original language | English |
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Article number | 1393 |
Number of pages | 24 |
Journal | Entropy |
Volume | 23 |
Issue number | 11 |
Early online date | 24 Oct 2021 |
DOIs | |
Publication status | Published - Nov 2021 |
Bibliographical note
This article is an open access article distributed under the terms andconditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Funding Information:
Acknowledgments: Eun-jin Kim acknowledges the Leverhulme Trust Research Fellowship (RF-2018-142-9) and thanks the collaborators, especially, James Heseltine who contributed to the works in this paper.
Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.
Funder
RF-2018-142-9Keywords
- Entropy
- Fluctuations
- Fokker-planck equation
- Information geometry
- Information length
- Information rate
- Langevin equations
- Self-organization
- Time-dependent probability density functions
ASJC Scopus subject areas
- Information Systems
- Mathematical Physics
- Physics and Astronomy (miscellaneous)
- Electrical and Electronic Engineering