This research identifies a **macroscopic physical law** governing the behavior of large language model (LLM)-driven agents. By analyzing state transitions as **Markov processes**, the authors discovered that these systems naturally satisfy a **detailed balance condition**, similar to physical systems in equilibrium. This suggests that LLMs do not merely follow rote strategies but instead learn internal **potential functions** that guide them toward optimal solutions. The study introduces a **least action principle** to quantify this directionality, allowing researchers to estimate an agent's global cognitive preferences. Through experiments with various models, the authors demonstrate that these dynamics remain consistent regardless of specific **architectures or prompt templates**. Ultimately, this work seeks to transform AI agent development from an engineering craft into a **predictable and quantifiable science**.