Benford's Law from Turing Ensembles and Integer Partitions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908669972578304 |
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| author | Kolpakov, Alexander Rocke, Aidan |
| author_facet | Kolpakov, Alexander Rocke, Aidan |
| contents | We develop two complementary generative mechanisms that explain when and why Benford's first-digit law arises. First, a probabilistic Turing machine (PTM) ensemble induces a geometric law for codelength. Maximizing its entropy under a constraint on halting length yields Benford statistics. This model shows a phase transition with respect to the halt probability. Second, a constrained partition model (Einstein-solid combinatorics) recovers the same logarithmic profile as the maximum-entropy solution under a coarse-grained entropy-rate constraint, clarifying the role of non-ergodicity (ensemble vs. trajectory averages). We also perform numerical experiments that corroborate our conclusions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16314 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Benford's Law from Turing Ensembles and Integer Partitions Kolpakov, Alexander Rocke, Aidan Information Theory Computational Complexity Discrete Mathematics Mathematical Physics H.1.1 We develop two complementary generative mechanisms that explain when and why Benford's first-digit law arises. First, a probabilistic Turing machine (PTM) ensemble induces a geometric law for codelength. Maximizing its entropy under a constraint on halting length yields Benford statistics. This model shows a phase transition with respect to the halt probability. Second, a constrained partition model (Einstein-solid combinatorics) recovers the same logarithmic profile as the maximum-entropy solution under a coarse-grained entropy-rate constraint, clarifying the role of non-ergodicity (ensemble vs. trajectory averages). We also perform numerical experiments that corroborate our conclusions. |
| title | Benford's Law from Turing Ensembles and Integer Partitions |
| topic | Information Theory Computational Complexity Discrete Mathematics Mathematical Physics H.1.1 |
| url | https://arxiv.org/abs/2502.16314 |