While language progresses through a sequence of semantic states, the underlying dynamics of this progression remain elusive. Here, we treat the semantic progression of written text as a stochastic trajectory in a high-dimensional state space. We utilize Allan deviation, a tool from precision metrology, to analyze the stability of meaning by treating ordered sentence embeddings as a displacement signal. Our analysis reveals two distinct dynamical regimes: short-time power-law scaling, which differentiates creative literature from technical texts, and a long-time crossover to a stability-limited noise floor. We find that while large language models successfully mimic the local scaling statistics of human text, they exhibit a systematic reduction in their stability horizon. These results establish semantic coherence as a measurable physical property, offering a framework to differentiate the nuanced dynamics of human cognition from the patterns generated by algorithmic models.

翻译：语言虽历经一系列语义状态的演进，但其背后的动力学机制仍不明确。本文将书面文本的语义演进视为高维状态空间中的随机轨迹，并采用精密计量学中的阿伦方差工具，通过将有序句子嵌入视作位移信号来分析意义的稳定性。分析揭示了两种截然不同的动力学机制：短期幂律标度行为（可区分创意文学与技术文本）以及长期向稳定性受限噪声底的交叉转变。研究发现，尽管大语言模型能成功模拟人类文本的局部标度统计特征，但其稳定性边界存在系统性缩减。这些结果确立了语义连贯性作为一种可测量的物理属性，为区分人类认知的精细动力学与算法模型生成模式提供了理论框架。