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arXiv · 2512.10047

Detailed balance in large language model-driven agents

Zhuo-Yang Song·Qing-Hong Cao·Ming-xing Luo·Hua Xing Zhu
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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.

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Zhuo-Yang Song, Qing-Hong Cao, Ming-xing Luo, Hua Xing Zhu. 2025-12-10. Detailed balance in large language model-driven agents. https://arxiv.org/abs/2512.10047

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