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Complexity measures, emergence, and multiparticle correlations.

Tobias Galla1, Otfried Gühne

  • 1Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester, United Kingdom. tobias.galla@manchester.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 12, 2012
PubMed
Summary
This summary is machine-generated.

This study questions existing correlation measures for complex systems, proposing a refined definition. The refined measure offers a more reliable quantification of correlations, even with local transformations or particle removal.

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Area of Science:

  • Complex Systems Science
  • Information Geometry
  • Statistical Mechanics

Background:

  • Existing correlation measures based on information geometry face challenges.
  • These measures can be sensitive to local transformations and particle removal, affecting their interpretation.
  • A robust quantification of correlations in complex systems is needed.

Purpose of the Study:

  • To critically evaluate recently proposed information geometry-based correlation measures.
  • To propose a refined correlation measure with improved properties for complex systems.
  • To investigate the impact of local transformations and coarse-graining on correlation measures.

Main Methods:

  • Information geometry
  • Analysis of local transformations
  • Study of particle discarding effects
  • Numerical evaluation of refined measures
  • Coupled logistic maps as a case study

Main Results:

  • Demonstrated that existing measures can increase under local transformations and particle removal.
  • Proposed a refined correlation measure with enhanced stability and interpretability.
  • Analyzed the behavior of different measures using coupled logistic maps.
  • Investigated effects of coarse-graining on correlation quantification.

Conclusions:

  • The refined correlation measure provides a more reliable quantification of complexity and correlations.
  • The study highlights the importance of considering local effects in complex systems analysis.
  • The proposed measure offers a robust tool for studying correlations in various complex systems.