发表机构
Institute for Physics and Astronomy, University of Potsdam（波茨坦大学物理与天文学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出广义龚珀茨定律的极简动力学模型，可统一描述帝国兴衰，通过14个帝国案例验证，发现行政成本累积为驱动衰落的核心机制，为大规模社会系统研究提供新定量原理。
AI 中文摘要
人类社会往往朝着规模扩大与复杂度提升的方向演化，随后常陷入停滞与衰落，历史上的帝国就是这一轨迹的典型范例。然而，现有定量模型多仅能捕捉扩张过程，极少在统一框架内解释衰落现象。本文提出一种极简动力学模型，可在单一形式体系中同时描述增长与崩溃过程；该模型能导出闭合形式轨迹，是对龚珀茨（Gompertz）定律的广义化，且具备等价的最大熵与最优控制表述。研究表明，该函数形式可刻画14个时间跨度差异极大的不同帝国的兴衰过程。尽管存在显著的历史异质性，所有案例均遵循由少量可解释参数支配的非对称上升-峰值-衰落模式。研究将此行为的驱动机制命名为“时间吞噬者（chronophage）”，即行政与协调成本呈指数级累积的负担，会抵消扩张带来的收益。这些发现揭示了一项通用定量原理，为理解复杂度提升如何约束大规模社会系统提供了新视角。
英文摘要
Human societies tend to evolve toward increasing scale and complexity, often followed by stagnation and decline. Historical empires provide a prominent example of this trajectory; however, existing quantitative models capture expansion and rarely account for decline within a unified framework. Here, we introduce a minimal dynamical model that describes both growth and collapse in a single formalism. The model yields a closed-form trajectory that generalizes the Gompertz law and admits equivalent maximum-entropy and optimal-control formulations. We show that this functional form captures the rise and fall of fourteen diverse empires across widely varying time scales. Despite substantial historical heterogeneity, all cases follow a common asymmetric rise-peak-decline pattern governed by a small number of interpretable parameters. We identify the mechanism driving this behavior as the chronophage: an exponentially accumulating burden of administrative and coordination costs that offsets the gains of expansion. These findings uncover a general quantitative principle, yielding new insights into how increasing complexity constrains large-scale social systems.
