对可持续性的无偏方法：从资本可替代性到非崩溃动力学
An Agnostic Approach to Sustainability: From Capitals Substitutability to Non-Collapse Dynamics
AI总结：
本文提出了一种随机动力学系统理论，通过分析资本可替代性和非崩溃动力学，探讨可持续性作为结构性边界属性的定义及其影响因素。
摘要：
我们构建了一种随机动力学系统理论，在其中可持续性是完全耦合的地球-人类-生产系统的一个结构性边界属性。每个子系统被建模为一个向量值过程，由具有乘性噪声和绝对双向子系统流动的随机微分方程所支配。生物多样性是内生的，社会评价由一个反射性函数表示，其权重取决于演进的人类能力。可持续性、发展和可持续发展被定义为轨迹属性。可持续性对应于正或单位概率下的边界非达成；发展对应于评价函数的局部上升；可持续发展要求在严格正生存概率下具有方向一致性。没有优化问题被施加。通过Feller边界分类和随机Lyapunov方法推导出必要和充分条件。一个中心结果确定了每个组件上的净绝对子系统流动的符号作为相变参数：如果在零附近为负，边界为退出类型，几乎确定性的持久性在结构上是不可能的，无论内在再生、能力积累或生产率参数如何。由于流动是绝对的，任何扰动都会通过整个耦合系统扩散，而无需相关外生冲击。反射性评价结构通常诱导非传递的发展关系，为路径依赖的福利比较提供正式机制。可持续性作为边界结构和向量场对齐的几何属性出现，而不是作为跨期最优性的推论。
英文摘要：
We construct a stochastic dynamical systems theory in which sustainability is a structural boundary property of a fully coupled Earth--Human--Production system. Each subsystem is modelled as a vector-valued process governed by stochastic differential equations with multiplicative noise and absolute bidirectional cross-subsystem flows. Biodiversity is endogenous, and societal evaluation is represented by a reflexive functional whose weights depend on evolving human capabilities. Sustainability, development, and sustainable development are defined as trajectory properties. Sustainability corresponds to boundary non-attainment with positive or unit probability; development corresponds to local ascent in the evaluation functional; sustainable development requires directional alignment under strictly positive survival probability. No optimisation problem is imposed. Necessary and sufficient conditions are derived using Feller boundary classification and stochastic Lyapunov methods. A central result identifies the sign of the net absolute cross-subsystem flow on each component as a phase-transition parameter: if negative near zero, the boundary is of exit type and almost-sure persistence is structurally impossible, independent of intrinsic regeneration, capability accumulation, or productivity parameters. Because flows are absolute, any perturbation diffuses through the entire coupled system without requiring correlated exogenous shocks. The reflexive evaluation structure generically induces non-transitive development relations, providing a formal mechanism for path-dependent welfare comparisons. Sustainability emerges as a geometric property of boundary structure and vector-field alignment, not as a corollary of intertemporal optimality.
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