受约束几何辐射的自组织
Self-Organization from Constrained Geometric Radiation
- School of Aeronautics and Astronautics, Shanghai Jiao Tong University（上海交通大学航空航天学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对封闭系统无外部驱动时自发产生动态有序的问题，提出耦合度规演化系统中通过几何辐射实现的约束诱导自组织，证明相关定理并验证其普适性，建立了封闭系统自组织的新范式。
AI中文摘要：
封闭系统中无外部驱动时如何自发产生动态有序？现有范式均要求外部能量流、温度淬灭或缓慢驱动。本文在耦合度规演化系统中报告了一种通过几何辐射实现的约束诱导自组织。模拟揭示了一个普适的四阶段循环：应力积累、超指数辐射、混沌坍缩，以及收敛至分形极限环——一种我们命名为楔形吸引子的新型吸引子拓扑，其具有五个量子化曲率态和分形微涨落。我们确定了四个联合充分条件：不可逆几何视界、量子相干性持续注入的应力、不相容曲率间的内生几何张力，以及有效涨落。它们的协同作用在视界边界触发临界雪崩。我们证明了三个定理：几何视界定理、几何能量耗散定理（暗示封闭系统中类波熵演化），以及辐射作为相变通道定理。我们进一步建立了约束诱导自组织定理：这些条件以概率1保证完整循环。系统扫描揭示了临界噪声阈值和辐射起始的幂律标度。我们在12种构型、多种噪声类型和三种几何流中验证了普适性。本工作为封闭系统自组织建立了新范式，在经典非线性约束与引力视界之间构建了精确数学对偶性。
英文摘要：
How does dynamic order emerge spontaneously in closed systems without external driving? Existing paradigms all require external energy flows, temperature quenching, or slow driving. Here we report constraint-induced self-organization via geometric radiation in coupled metric evolution systems. Simulations reveal a universal four-stage cycle: stress accumulation, super-exponential radiation, chaotic collapse, and convergence to a fractal limit cycle, a novel attractor topology we term the wedge-shaped attractor, with five quantized curvature states and fractal micro-fluctuations. We identify four jointly sufficient conditions: an irreversible geometric horizon, persistent stress injection from quantum coherence, endogenous geometric tension between incompatible curvatures, and effective fluctuations. Their synergy triggers a critical avalanche at the horizon boundary. We prove three theorems: the Geometric Horizon Theorem, the Geometric Energy Dissipation Theorem (implying wave-like entropy evolution in closed systems), and the Radiation as Phase Transition Channel Theorem. We further establish the Constraint-Induced Self-Organization Theorem: these conditions guarantee the complete cycle with probability one. Systematic scans reveal a critical noise threshold and power-law scaling of radiation onset. We verify universality across 12 configurations, multiple noise types, and three geometric flows. This work establishes a new paradigm for closed-system self-organization, forging an exact mathematical duality between classical nonlinear constraints and gravitational horizons.
