结构形态与引力时间箭头
Structural morphology and the gravitational arrow of time
AI总结：
研究牛顿N体问题中，全局尺度不变聚类对比度V相近的两个N=5000中心构型，局部各向异性差异显著，揭示V无法唯一确定形态，需结合局部关系可观测量补充描述。
AI中文摘要：
零能量、零线动量、零角动量扇区的牛顿N体问题提供了时间反演不变的场景，其中一般完整解具有雅努斯点（Janus point），并在远离该点的两个分支上呈现引力箭头。无量纲量V是一种全局尺度不变的聚类对比度度量，它并非逐点单调，而是在远离雅努斯区域的上升边界之间增长时波动。中心构型是同一尺度不变景观的临界形状，因此可作为探究V所编码结构信息的可控探针。我们利用数值粒子坐标数据，针对两个平面N=5000的中心构型研究该问题。局部形态由六邻各向异性A₆量化，其取值范围为：各向同性局部环境对应0，有效一维环境对应1。尽管两种构型的V值仅相差1.686%，但它们的平均各向异性相差156.8%，分别为0.1331和0.3419；此外，V值较高的构型中有18.1%的粒子满足A₆>0.5，而V值较低的构型中无此类粒子。该各向异性排序在所有测试的邻域大小4≤k≤12中均保持，且主对比度通过了无量纲近邻鲁棒性测试。因此，对于这对临界形状，全局V值的相近值对应着显著不同的局部几何组织，这表明其长期行为表征BKM引力箭头的标量量本身并不能唯一确定形态，从而将局部关系可观测量识别为补充描述层面，为静态形状空间景观与真实雅努斯点历史的形态之间提供了定量桥梁。
英文摘要：
The Newtonian $N$-body problem in the zero-energy, zero-linear-momentum, and zero-angular-momentum sector provides a time-reversal-invariant setting in which generic complete solutions possess a Janus point and exhibit a gravitational arrow on both branches away from it. The dimensionless variety $V$, a global scale-invariant measure of clustering contrast, is not pointwise monotonic but fluctuates while growing between rising bounds away from the Janus region. Central configurations are critical shapes of the same scale-invariant landscape and therefore provide controlled probes of the structural information encoded by $V$. We investigate this question for two planar $N=5000$ central configurations using the numerical particle-coordinate data. Local morphology is quantified by the six-neighbour anisotropy $A_6$, which ranges from $0$ for an isotropic local environment to $1$ for an effectively one-dimensional one. Although the varieties of the two configurations differ by only $1.686\%$, their mean anisotropies differ by $156.8\%$, from $0.1331$ to $0.3419$. Moreover, $18.1\%$ of the particles in the higher-variety configuration satisfy $A_6>0.5$, whereas none do so in the lower-variety configuration. The anisotropy ordering persists for all tested neighbourhood sizes $4\le k\le12$, and the principal contrast survives a dimensionless close-pair robustness test. For this pair of critical shapes, nearby values of the global variety therefore coexist with markedly different local geometrical organization. Thus the scalar quantity whose long-term behavior characterizes the BKM gravitational arrow does not, by itself, uniquely specify morphology. This identifies local relational observables as a complementary level of description and provides a quantitative bridge between the static shape-space landscape and morphology along genuine Janus-point histories.
