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

## TL;DR

This paper explores how combining multiple components can create systems with unexpectedly high structural complexity.

## Contribution

The paper introduces a new kind of structural complexity in multicomponent systems that goes beyond statistical mixtures.

## Key findings

- Multicomponent systems can be infinitely more complex than their individual parts.
- Statistical mixtures fail to capture emergent hierarchical structures in these systems.
- The study reveals implications for system ergodicity due to this new structural complexity.

## Abstract

We show that mixtures comprising 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.