Information geometric methods for complexity
Domenico Felice1, Carlo Cafaro2, Stefano Mancini3
1Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany.
Chaos (Woodbury, N.Y.)
|April 2, 2018
Summary
Information geometry (IG) provides novel complexity measures for classical and quantum physics. These methods analyze phase transitions, network complexity, and entropic motion using geometric concepts like curvature and volume.
Area of Science:
- Physics
- Information Geometry
- Complexity Science
Background:
- Recent advances in information geometry (IG) offer new tools for physics.
- Complexity measures are crucial for understanding physical systems.
Purpose of the Study:
- To review the application of IG methods for defining complexity measures in classical and quantum physics.
- To explore how geometric concepts describe phase transitions and network complexity.
Main Methods:
- Utilizing scalar curvature and metric tensor components to analyze phase transitions.
- Employing Riemannian volume of parameter spaces for network complexity.
- Investigating entropic motion on curved statistical manifolds.
Main Results:
- IG methods successfully define complexity measures across various physical settings.
- Geometric properties of parameter manifolds reveal insights into phase transitions and system dynamics.
- Kullback-Leibler divergence and manifold volumes are key IG notions for complexity.
Conclusions:
- IG offers a powerful geometric framework for quantifying complexity in physics.
- The review highlights strengths, limitations, and future directions for IG in complexity research.
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