Algorithmic Temperature Induced by Adopted Regular Universal Turing Machine

Kentaro Imafuku

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arXiv · 2510.11737

Algorithmic Temperature Induced by Adopted Regular Universal Turing Machine

Kentaro Imafuku

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Abstract

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.

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cond-mat.stat-mech cs.IT math.IT quant-ph

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Kentaro Imafuku. 2025-10-10. Algorithmic Temperature Induced by Adopted Regular Universal Turing Machine. https://arxiv.org/abs/2510.11737

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