Algorithmic Temperature Induced by Adopted Regular Universal Turing Machine
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909849402474496 |
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| author | Imafuku, Kentaro |
| author_facet | Imafuku, Kentaro |
| contents | We prove that an effective temperature naturally emerges from the algorithmic structure of a regular universal Turing machine (UTM), without introducing any external physical parameter. In particular, the redundancy growth of the machine's wrapper language induces a Boltzmann--like exponential weighting over program lengths, yielding a canonical ensemble interpretation of algorithmic probability. This establishes a formal bridge between algorithmic information theory and statistical mechanics, in which the adopted UTM determines the intrinsic ``algorithmic temperature.'' We further show that this temperature approaches its maximal limit under the universal mixture (Solomonoff distribution), and discuss its epistemic meaning as the resolution level of an observer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11737 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algorithmic Temperature Induced by Adopted Regular Universal Turing Machine Imafuku, Kentaro Statistical Mechanics Information Theory Quantum Physics We prove that an effective temperature naturally emerges from the algorithmic structure of a regular universal Turing machine (UTM), without introducing any external physical parameter. In particular, the redundancy growth of the machine's wrapper language induces a Boltzmann--like exponential weighting over program lengths, yielding a canonical ensemble interpretation of algorithmic probability. This establishes a formal bridge between algorithmic information theory and statistical mechanics, in which the adopted UTM determines the intrinsic ``algorithmic temperature.'' We further show that this temperature approaches its maximal limit under the universal mixture (Solomonoff distribution), and discuss its epistemic meaning as the resolution level of an observer. |
| title | Algorithmic Temperature Induced by Adopted Regular Universal Turing Machine |
| topic | Statistical Mechanics Information Theory Quantum Physics |
| url | https://arxiv.org/abs/2510.11737 |