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Main Author: Imafuku, Kentaro
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2510.11737
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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