Algorithmic Temperature Induced by Adopted Regular Universal Turing Machine

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.