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arXiv · 2507.07343

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

James P. Crutchfield
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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.

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James P. Crutchfield. 2025-07-10. Way More Than the Sum of Their Parts: From Statistical to Structural Mixtures. https://arxiv.org/abs/2507.07343

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