Way More Than the Sum of Their Parts: From Statistical to Structural Mixtures

TL;DR

This paper reveals that multicomponent systems exhibit a level of structural complexity far exceeding simple statistical mixtures, highlighting emergent hierarchical organization and implications for system ergodicity.

Contribution

It introduces a new concept of structural complexity in multicomponent systems, contrasting it with traditional statistical mixture models.

Findings

Multicomponent systems are often infinitely more complex structurally than their statistical counterparts.

Statistical mixtures fail to capture the hierarchical organization in multicomponent systems.

The work has broad implications for understanding system ergodicity.

Abstract

We show that mixtures comprised of multicomponent systems typically are much more structurally complex than the sum of their parts; sometimes, infinitely more complex. We contrast this with the more familiar notion of statistical mixtures, demonstrating how statistical mixtures miss key aspects of emergent hierarchical organization. This leads us to identify a new kind of structural complexity inherent in multicomponent systems and to draw out broad consequences for system ergodicity.