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Computer Science > Machine Learning

arXiv:2512.10047 (cs)
[Submitted on 10 Dec 2025]

Title:Detailed balance in large language model-driven agents

Authors:Zhuo-Yang Song, Qing-Hong Cao, Ming-xing Luo, Hua Xing Zhu
View a PDF of the paper titled Detailed balance in large language
model-driven agents, by Zhuo-Yang Song and 3 other authors
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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.

Comments: 20 pages, 12 figures, 5 tables
          Machine Learning (cs.LG); Statistical Mechanics
Subjects: (cond-mat.stat-mech); Artificial Intelligence (cs.AI);
          Adaptation and Self-Organizing Systems (nlin.AO); Data
          Analysis, Statistics and Probability (physics.data-an)
Cite as:  arXiv:2512.10047 [cs.LG]
          (or arXiv:2512.10047v1 [cs.LG] for this version)
          https://doi.org/10.48550/arXiv.2512.10047
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Zhuo-Yang Song [view email]
[v1] Wed, 10 Dec 2025 20:04:23 UTC (409 KB)
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