Biological swarms, such as ant colonies, achieve collective goals through decentralized and stochastic individual behaviors. Similarly, physical systems composed of gases, liquids, and solids exhibit random particle motion governed by entropy maximization, yet do not achieve collective objectives. Despite this analogy, no unified framework exists to explain the stochastic behavior in both biological and physical systems. Here, we present empirical evidence from \textit{Formica polyctena} ants that reveals a shared statistical mechanism underlying both systems: maximization under different energy function constraints. We further demonstrate that robotic swarms governed by this principle can exhibit scalable, decentralized cooperation, mimicking physical phase-like behaviors with minimal individual computation. These findings established a unified stochastic model linking biological, physical, and robotic swarms, offering a scalable principle for designing robust and intelligent swarm robotics.

翻译：生物集群（如蚁群）通过去中心化且随机的个体行为实现集体目标。类似地，由气体、液体和固体组成的物理系统表现出受熵最大化支配的随机粒子运动，但并未达成集体目标。尽管存在这种类比，目前尚无统一框架来解释生物与物理系统中的随机行为。本文通过\textit{Formica polyctena}蚂蚁的实验证据，揭示了两类系统共有的统计机制：在不同能量函数约束下的最大化原理。我们进一步证明，遵循该原理的机器人集群能够展现出可扩展的去中心化协作，以极少的个体计算模拟类似物理相变的行为。这些发现建立了一个连接生物、物理与机器人集群的统一随机模型，为设计鲁棒且智能的集群机器人提供了可扩展的理论基础。