Way More Than the Sum of Their Parts: From Statistical to Structural Mixtures
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911048525676544 |
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| author | Crutchfield, James P. |
| author_facet | Crutchfield, James P. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07343 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Way More Than the Sum of Their Parts: From Statistical to Structural Mixtures Crutchfield, James P. Statistical Mechanics Machine Learning Dynamical Systems Statistics Theory Chaotic Dynamics 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. |
| title | Way More Than the Sum of Their Parts: From Statistical to Structural Mixtures |
| topic | Statistical Mechanics Machine Learning Dynamical Systems Statistics Theory Chaotic Dynamics |
| url | https://arxiv.org/abs/2507.07343 |