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

Area of Science:

• Interdisciplinary applications of information theory and information geometry.
• Focus on non-equilibrium thermodynamics and statistical physics.
• Relevance to astrophysical, plasma, and biological systems.

Background:

• Information theory offers a framework for analyzing complex phenomena across diverse scientific fields.
• Information geometry quantifies process evolution via probability density function (PDF) changes over time.
• Non-equilibrium processes exhibit dynamic characteristics like time-varying mean, variance, or temperature.

Purpose of the Study:

• To explore recent advancements in information geometric theory for dynamic non-equilibrium processes.
• To analyze the thermodynamic and physical/biological implications of these dynamic aspects.
• To highlight the significance of path-dependent distances for time-varying PDFs.

Main Methods:

• Comparing various distance metrics between probability density functions (PDFs).
• Investigating the role of information rate (Γ = dL/dt) and relative entropy.
• Analyzing information length (L) as a measure of distinguishable states over time.
• Examining geodesic solutions within information geometry.

Main Results:

• Emphasizing the importance of path-dependent distances for time-dependent PDFs.
• Demonstrating the utility of information rate and relative entropy in non-equilibrium thermodynamics.
• Establishing inequalities among thermodynamic quantities like entropy production and heat flux.
• Identifying potential implications of geodesic solutions for self-organization and control.

Conclusions:

• Information geometry provides a powerful lens for understanding dynamic non-equilibrium systems.
• The study underscores the link between information-theoretic measures and thermodynamic principles.
• Geodesic paths in information geometry may offer fundamental insights into emergent order and regulation.