Title: Algorithmic Temperature Induced by Adopted Regular Universal Turing Machine Show Chinese title

Title: 算法温度由采用的通用图灵机引起

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. Show Chinese abstract

Abstract: 我们证明，有效温度自然地从常规通用图灵机（UTM）的算法结构中产生，而无需引入任何外部物理参数。 特别是，该机器包装语言的冗余增长会在程序长度上产生类似玻尔兹曼的指数权重，从而对算法概率进行规范系综解释。 这在算法信息论和统计力学之间建立了一个正式的桥梁，在此过程中所采用的UTM决定了内在的“算法温度”。 我们进一步表明，这种温度在通用混合（Solomonoff分布）下趋近于其最大极限，并讨论了它作为观察者分辨水平的认知意义。