# Detailed balance in large language model-driven agents

arXiv: https://arxiv.org/abs/2512.10047 · HTML: https://mlsanity.com/paper/2512.10047/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 12 of its 23 references that are in the map.
- First posted on arXiv 10 Dec 2025.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 12 of 12)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Voyager: An Open-Ended Embodied Agent with Large Language Models](https://mlsanity.com/paper/2305.16291/) (2023)
- [Code as Policies: Language Model Programs for Embodied Control](https://mlsanity.com/paper/2209.07753/) (2022)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Plan-and-Solve Prompting: Improving Zero-Shot Chain-of-Thought Reasoning by Large Language Models](https://mlsanity.com/paper/2305.04091/) (2023)
- [AI Agents vs. Agentic AI: A Conceptual Taxonomy, Applications and Challenges](https://mlsanity.com/paper/2505.10468/) (2025)
- [Phase Transitions in Large Language Models and the O(N) Model](https://mlsanity.com/paper/2501.16241/) (2025)
- [Neural Thermodynamic Laws for Large Language Model Training](https://mlsanity.com/paper/2505.10559/) (2025)
- [Scalable Quantum State Preparation via Large-Language-Model-Driven Discovery](https://mlsanity.com/paper/2505.06347/) (2025)

## Built on by (most cited first, 6 of 6)

- [Collective Alignment in LLM Multi-Agent Systems: Disentangling Bias from Cooperation via Statistical Physics](https://mlsanity.com/paper/2605.10528/) (2026)
- [A Theoretical Lens for RL-Tuned Language Models via Energy-Based Models](https://mlsanity.com/paper/2512.18730/) (2025)
- [Microscopic dynamics of consensus formation in multi-agent LLM Naming Games](https://mlsanity.com/paper/2608.02178/) (2026)
- [A Theory of LLM Information Susceptibility](https://mlsanity.com/paper/2603.23626/) (2026)
- [Interaction Creates Dynamical AI Behavior Absent in Isolation](https://mlsanity.com/paper/2608.07457/) (2026)
- [On the Structural Limits of Machine Learning Decision Systems: An Information-Theoretic, Interaction-Based, and Stochastic-Dynamical Perspective](https://mlsanity.com/paper/2608.13510/) (2026)

## Abstract (arXiv)

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.