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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
PubMed
Summary
This summary is machine-generated.

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.

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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.