An Algorithmic Approach to Emergence

TL;DR

This paper introduces an objective, algorithmic information theory-based framework to quantify emergence, identifying drops in the Kolmogorov structure function as key indicators, with applications to dynamical systems and thermodynamics.

Contribution

It proposes a novel, quantitative definition of emergence using Kolmogorov complexity, extending coarse-graining and boundary concepts, and applies it to complex systems.

Findings

Identification of drops in the Kolmogorov structure function as emergence indicators

Extension of coarse-graining and boundary condition notions

Application to dynamical systems and thermodynamics

Abstract

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.