Way More Than the Sum of Their Parts: From Statistical to Structural Mixtures
This addresses foundational issues in complexity theory for researchers in fields like physics and AI, though it appears incremental by contrasting with existing statistical mixture concepts.
The paper tackles the problem of understanding structural complexity in multicomponent systems, showing that mixtures can be infinitely more complex than the sum of their parts, with implications for system ergodicity.
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.