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Making sense of complex systems through resolution, relevance, and mapping entropy
Roi Holtzman1, Marco Giulini2,3, Raffaello Potestio2,3
1Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel.
Physical Review. E
|November 18, 2022
Summary
This study introduces a quantitative method to identify key components in complex systems. The approach uses statistical information measures to select degrees of freedom that best represent the system's underlying generative process.
Area of Science:
- Complex systems science
- Statistical physics
- Information theory
Background:
- Complex systems exhibit emergent properties due to intricate interactions.
- Identifying dominant degrees of freedom in such systems is challenging.
- Understanding these key components is crucial for system analysis.
Purpose of the Study:
- To develop a quantitative method for identifying and selecting essential degrees of freedom in complex systems.
- To establish novel connections between statistical information measures.
- To provide a generalizable approach applicable to diverse complex systems.
Main Methods:
- Utilizing three statistical information measures: resolution, relevance, and mapping entropy.
- Analyzing the interrelations between these measures.
- Developing a method to quantify the selection of degrees of freedom preserving maximal information content.
Main Results:
- Established novel connections between resolution and mapping entropy.
- Demonstrated a quantitative method to identify the number and selection of degrees of freedom.
- Successfully applied the method to diverse systems including spin models, financial markets, and protein simulations.
Conclusions:
- The developed method provides a robust framework for analyzing complex systems.
- It enables the identification of critical degrees of freedom that capture the system's dynamics.
- The freely available software facilitates broader application in scientific research.
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