Quantifying emergent complexity

Area of Science:

• Complex Systems Science
• Theoretical Physics
• Information Theory

Background:

• Complex systems exhibit multiscale causal structures, from microphysics to macroeconomics.
• The added value of macroscale descriptions beyond data compression is debated.
• Understanding irreducible causal contributions across scales is crucial for systems science.

Purpose of the Study:

• To introduce a new theory of emergence capable of distinguishing scales with irreducible causal contributions.
• To resolve the debate on the functional role of macroscales in complex systems.
• To develop a novel measure for emergent complexity.

Main Methods:

• Developed a new theoretical framework for emergence.
• Applied the theory to coarse-grained Markov chains.
• Quantified causal contributions across a hierarchy of scales.

Main Results:

• Introduced a novel theory distinguishing scales with irreducible causal influence.
• Demonstrated the theory's application using Markov chains.
• Revealed a new measure of emergent complexity: the distribution of causal contributions across scales.

Conclusions:

• The new theory provides a rigorous method to identify essential scales in complex systems.
• Emergent complexity can be quantified by the breadth of causal influence distribution.
• This framework advances our understanding of multiscale causality and system organization.