An Algorithmic Approach to Emergence
This work addresses the challenge of objectively measuring emergence in complex systems, which is foundational for fields like physics and AI, though it appears incremental as it builds on existing algorithmic information theory concepts.
The paper tackles the problem of defining emergence quantitatively by proposing an algorithmic information theory framework that identifies emergence through drops in the Kolmogorov structure function of observational data, and it provides theoretical results and applications to dynamical systems and thermodynamics.
We suggest a quantitative and objective notion of emergence. Our proposal uses algorithmic information theory as a basis for an objective framework in which a bit string encodes observational data. A plurality of drops in the Kolmogorov structure function of such a string is seen as the hallmark of emergence. Our definition offers some theoretical results, in addition to extending the notions of coarse-graining and boundary conditions. Finally, we confront our proposal with applications to dynamical systems and thermodynamics.