2025/12/10 by Zhuo-Yang Song, Song, Zhuo-Yang, Qing-Hong Cao +6 · 3 voices · 1 citation
Computer Science · Materials Science · Social Sciences · #Language and cultural evolution #Machine Learning in Materials Science #Topic Modeling #cond-mat.stat-mech #cs.AI #cs.LG #nlin.AO #physics.data-an
paper · pdf · doi:10.48550/arxiv.2512.10047
openalex publication_date 2025/12/10 · openalex created_date 2025/12/13 · openalex updated_date 2026/07/28
Large language model (LLM)-driven agents are emerging as a powerful new paradigm for solving complex problems. Despite the empirical success of these practices, a theoretical framework to understand and unify their macroscopic dynamics remains lacking. This Letter proposes a method based on the least action principle to estimate the underlying generative directionality of LLMs embedded within agents. By experimentally measuring the transition probabilities between LLM-generated states, we statistically discover a detailed balance in LLM-generated transitions, indicating that LLM generation may not be achieved by generally learning rule sets and strategies, but rather by implicitly learning a class of underlying potential functions that may transcend different LLM architectures and prompt templates. To our knowledge, this is the first discovery of a macroscopic physical law in LLM generative dynamics that does not depend on specific model details. This work is an attempt to establish a macroscopic dynamics theory of complex AI systems, aiming to elevate the study of AI agents from a collection of engineering practices to a science built on effective measurements that are predictable and quantifiable.