Asymptotic Information-Theoretic Detection of Dynamical Organization in Complex Systems

Area of Science:

• Complex Systems Science
• Computational Biology
• Theoretical Chemistry

Background:

• Identifying emergent structures in complex dynamical systems is a significant scientific challenge.
• Existing methods often require extensive simulations, limiting their applicability to large systems.

Purpose of the Study:

• To propose a computationally efficient methodology for identifying emergent structures in complex dynamical systems.
• To develop a novel sieving algorithm for navigating variable subsets and comparing them using a simulation-free index.

Main Methods:

• Modeling system states as random variables.
• Implementing a sieving algorithm to explore subsets of variables.
• Utilizing an information-theoretic measure of coordination to derive a comparison index, analyzed via its asymptotic distribution under no coordination.

Main Results:

• A computationally efficient method for identifying emergent structures was developed.
• The proposed index allows fair comparison of variable subsets with varying sizes.
• The number of observations directly correlates with the ability to identify larger emergent subsets.

Conclusions:

• The methodology provides an efficient way to detect emergent structures in complex dynamical systems.
• The approach is applicable to diverse fields, including the study of autocatalytic sets relevant to the origin of life.