Quantifying emergent complexity
Year: 2026
Type: article
Abstract: Complex systems can be described at myriad different scales, and their causal workings often have a multiscale structure (e.g., a computer can be described at the microscale of its hardware circuitry, the mesoscale of its machine code, and the macroscale of its operating system). While scientists study and model systems across the full hierarchy of their scales, from microphysics to macroeconomics, there is debate about what the macroscales of systems can possibly add beyond mere compression. To resolve this long-standing issue, here, a new theory of emergence is introduced that can distinguish which scales irreducibly contribute to a system's causal workings. The theory's application is demonstrated in coarse grains of Markov chains, revealing a novel measure of emergent complexity: how widely distributed a system's causal contributions are across its hierarchy of scales.
Source: Patterns
Author: Erik Hoel
Institution: Tufts University
Language: English
Topic: Complex Systems and Dynamics
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $4,900
OpenAlex ID: W7120043890