{"ID":2830878,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.10047","arxiv_id":"2512.10047","title":"Detailed balance in large language model-driven agents","abstract":"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.","short_abstract":"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 t...","url_abs":"https://arxiv.org/abs/2512.10047","url_pdf":"https://arxiv.org/pdf/2512.10047v1","authors":"[\"Zhuo-Yang Song\",\"Qing-Hong Cao\",\"Ming-xing Luo\",\"Hua Xing Zhu\"]","published":"2025-12-10T20:04:23Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cond-mat.stat-mech\",\"cs.AI\",\"nlin.AO\",\"physics.data-an\"]","methods":"[\"Large Language Model\",\"Language Model\"]","has_code":false}