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A Statistical Physics Characterization of the Complex Systems Dynamics: Quantifying Complexity from Spatio-Temporal

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This study introduces a new framework to measure complexity in biological systems by analyzing collective motion. The developed method quantifies emergence and self-organization, revealing insights into natural animal group dynamics.

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Area of Science:

  • Complex Systems Biology
  • Theoretical Biology
  • Biophysics

Background:

  • Biological systems exhibit complex behaviors, generating spatio-temporal structures from seemingly random interactions.
  • Existing research lacks a quantifiable framework to measure the complexity of these biological systems.
  • Understanding collective motion is crucial for deciphering emergent properties in nature.

Purpose of the Study:

  • To develop a novel, quantifiable framework for measuring complexity in collective motion of biological systems.
  • To identify spatio-temporal states, transition probabilities, and free energy landscapes of collective movement.
  • To quantify emergence, self-organization, and missing information based on the energy landscape.

Main Methods:

  • Developed a new paradigm to analyze collective motion of N agents in 3D space.
  • Identified spatio-temporal states and their transition probabilities.
  • Estimated free energy landscapes to quantify system properties.

Main Results:

  • Collective motion evolves towards states with lower energy and reduced missing information.
  • Quantified emergence, self-organization, and complexity in collective motion.
  • Natural animal groups demonstrate increasing emergence, self-organization, and complexity over time.

Conclusions:

  • The developed framework provides a quantitative measure for complexity in biological systems.
  • The study elucidates the dynamics of collective motion, highlighting convergence to optimal states.
  • The algorithm can be applied to engineer collective behaviors with desired emergent properties.