从冻结到终端堆积：一个谜题与一个悖论
From Freezing to Terminal Packing: A Puzzle and a Paradox
AI总结：
该研究重新审视Ramakrishnan-Yussouff分岔框架，通过密度泛函理论发现亚稳态液体的有限波矢热力学边际性，揭示液体关联编码终端无序堆积趋近过程的谜题。
AI中文摘要：
针对平衡冻结发展的密度泛函理论，也能产生接近终端堆积的高密度端点。我们重新审视非线性Ramakrishnan-Yussouff分岔框架，区分出首个晶态折叠、热力学共存与终端边际性。在终端点，巨势沿主有限波矢密度模式的曲率消失，恰好对应非线性自洽方程失去刚性。该构造给出一维硬杆的精确密堆积、硬盘终端堆积分数约0.8407，以及接近随机密堆积的硬球值约0.629。这些结果表明，这是亚稳态液体延续的有限波矢热力学边际性，而非平衡冻结或机械堵塞，同时揭示了一个持久谜题：为何液体态关联能编码不同物理维度与系统中终端无序堆积的趋近过程？
英文摘要：
A density-functional theory developed for equilibrium freezing also produces a high-density endpoint close to terminal packing. We revisit the nonlinear Ramakrishnan--Yussouff bifurcation framework and distinguish the first crystalline fold, thermodynamic coexistence, and terminal marginality. At the terminal point, the grand-potential curvature vanishes along the principal finite-wavevector density mode, exactly when the nonlinear self-consistency equation loses stiffness. The construction gives exact close packing for one-dimensional hard rods, a terminal hard-disk packing fraction near 0.8407, and a hard-sphere value near 0.629, close to random close packing. These results identify a finite-wavevector thermodynamic marginality of a metastable liquid continuation, rather than equilibrium freezing or mechanical jamming, and expose a persistent puzzle: why should liquid-state correlations encode the approach to terminal disordered packing across different physical dimensions and systems?
