这篇论文用‘权力’和‘响应函数’两个变量就能拆解集体智能的涌现机制，还给出了最优秩序公式，想从底层理解多智能体系统的话可以一读。
该论文提出了一个通用框架，分析智能体行动与集体观测间有反馈回路的系统，基于两个变量：权力（衡量智能体对集体结果的影响）和响应函数（决定智能体如何反应）。推导了总权力、有用权力、熵、秩序、脆弱性和移动性等宏观属性从这两个变量涌现的方式。引入一个由风险偏好系数参数化的系统级效用函数，推导了在生产率、稳定性和适应性间平衡的最优秩序度。分析表明，更强的同步化可能增加集体产出，但也增加脆弱性并降低移动性。该框架通过测量和设计权力分布与响应函数，有助于理解和优化集体行为。
Optimal Order of Multi-Agent and General Many-Body Systems
This paper develops a general framework for analyzing multi-agent systems with feedback loops between agents actions and collective observations. The framework is built on two fundamental agent-level variables: power, which measures agent influence on collective outcomes, and response functions, which determine how agents react to observations. We derive how macroscopic properties, including total power, useful power, entropy, order, fragility, and mobility, emerge from these two variables of heterogeneous agents. To study the trade off between growth and resilience, we introduce a system-level utility function parameterized by a risk-appetite coefficient and derive an optimal degree of order that balances productivity, stability, and adaptability. The analysis suggests that stronger synchronization can increase collective output but may also increase systemic fragility and reduce mobility. We further argue that order, entropy, information, and useful energy are task-dependent and system-relative concepts whose meanings depend on the objectives of the system. By measuring and designing agent power distributions and response functions, it may be possible to better understand, predict, and optimize collective behavior and identify the conditions under which collective intelligence and optimal order emerge.