AI 中文总结
该研究将行星可持续性建模为耦合资源与废物动态的非平衡问题，提出含两类阈值的非线性模型，关联多个相关理论，指出承载力是随时间变化的涌现属性。
AI 中文摘要
地球在物质层面近乎封闭，但在能量层面是开放的。我们将行星可持续性表述为耦合有限存量与流量的最小非平衡动力学问题，采用封闭生态系统与工程生命支持系统的操作语言：存量、流量平衡、回收效率、处理能力、储备时间及失效阈值。该框架围绕两个有限缓冲构建：可耗竭的资源存量与可饱和的废物处理能力。禁食与肾衰竭的生理差异催生了储备时间原则：主导约束是最先达到临界状态的缓冲。由此得到的非线性模型耦合了可再生资源存量、累积废物存量与总活动变量，呈现出两类阈值：软废物阈值（累积废物抑制增长但处理能力仍充足）与硬阈值（废物产生量超过最大处理能力）。我们将模型扩展至回收及多类资源与废物，给出明确的简化数值示例，并将该方法与“地球号宇宙飞船”、行星边界、《增长的极限》及存量-污染增长模型相关联。多尺度类比——细胞、有机体、行星——强调生命支持功能分布于降解、回收、运输、调节与清除过程。核心主张是有条件的：承载力是资源、废物、回收、技术与制度动态耦合的涌现性、随时间变化的属性；资源耗竭或废物处理失效均可成为约束条件，取决于它们的特征储备时间。
英文摘要
Earth is nearly closed with respect to matter but open with respect to energy. We formulate planetary sustainability as a minimal nonequilibrium dynamical problem for coupled finite stocks and fluxes, using the operational language of closed ecological and engineered life-support systems: inventories, flux balances, recycling efficiencies, processing capacities, reserve times, and failure thresholds. The framework describes a competition between two finite buffers: resource stocks that can be depleted and waste-processing capacities that can be saturated. The physiological contrast between fasting and renal failure motivates a general reserve-time principle: the dominant constraint is the buffer that becomes critical first. Our nonlinear model couples a regenerative resource stock, an accumulated waste stock, and an aggregate activity variable. It exhibits a soft waste threshold, where accumulated waste suppresses growth while processing remains formally capable, and a hard threshold, where waste production exceeds maximal processing capacity. We extend the model to recycling and multiple resource and waste classes, give an explicit numerical example, and relate it to Spaceship Earth, planetary boundaries, Limits to Growth, and stock-pollution growth models. A multiscale analogy--cell, organism, planet--emphasizes that life-support functions combine degradation, recycling, transport, regulation, and removal. Carrying capacity thus emerges as a time-dependent property of coupled resource, waste, recycling, technological, and institutional dynamics: either resource depletion or elimination failure may become the binding constraint, depending on their characteristic reserve times.
Comments13 pages, 1 figure
