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Published on: September 23, 2025
Mutual information as a tool for identifying phase transitions in dynamical complex systems with limited data.
R T Wicks1, S C Chapman, R O Dendy
1Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry, UK.
Summary
Mutual information effectively detects order-disorder transitions in flocking systems, even with limited particle tracking and data. This method proves more sensitive than susceptibility for identifying phase transition locations.
Area of Science:
- Complex systems
- Statistical physics
- Information theory
Background:
- Flocking behavior in nature and physics models exhibits order-disorder transitions.
- Detecting these transitions is crucial for understanding collective dynamics.
- Traditional methods may struggle with limited observational data.
Purpose of the Study:
- To evaluate mutual information as a sensitive tool for detecting order-disorder phase transitions.
- To assess the efficacy of mutual information under conditions of limited observations.
- To identify key dimensionless parameters governing flocking transitions.
Main Methods:
- Utilized the established Vicsek model for flocking dynamics.
- Applied mutual information analysis to system data.
- Compared mutual information's performance against susceptibility measures.
Main Results:
- Mutual information accurately pinpoints phase transition locations.
- It remains effective even with sparse tracking of particles.
- Partial data (position/velocity components) does not hinder its sensitivity.
- Identified natural dimensionless parameters crucial for the transition.
Conclusions:
- Mutual information is a robust indicator for flocking order-disorder transitions.
- It outperforms susceptibility when data is limited or incomplete.
- This approach enhances the study of complex systems with partial observability.
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