标题： 自组织系统中平均动作效率通过随机最小作用量动力学单调上升 显示英文标题

标题： Average Action Efficiency Rises Monotonically in Self-Organizing Systems via Stochastic Least-Action Dynamics

摘要： 自组织系统将噪声运动转化为高效结构，但缺乏一种通用的、无量纲的度量方法。 我们从随机路径积分最小作用原理中推导出平均作用效率（AAE）——每总作用的事件数。 一个李雅普诺夫恒等式将其单调上升与作用方差和噪声减少速率联系起来，定义了增长、饱和和衰减阶段。 基于代理的蚂蚁觅食和单分子ATP合成酶数据验证了预测的S型上升和平台。 由于AAE只需要事件计数和积分作用，它为跨物理、化学、生物和活性物质的反馈控制自组织提供了一种轻量级度量和设计规则。 显示英文摘要

摘要： Self-organizing systems convert noisy motion into efficient structure, yet a universal, dimensionless measure of this transformation is lacking. We derive the Average Action Efficiency (AAE) - events per total action - from a stochastic path-integral least-action principle. A Lyapunov identity links its monotonic rise to the action variance and the rate of noise reduction, defining growth, saturation, and decay regimes. Agent-based ant foraging and single-molecule ATP-synthase data confirm the predicted sigmoidal rise and plateau. Because AAE needs only an event count and an integrated action, it offers a lightweight metric and design rule for feedback-controlled self-organization across physics, chemistry, biology, and active matter.