From Freezing to Terminal Packing: A Puzzle and a Paradox

Biman Bagchi

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arXiv · 2608.29676

From Freezing to Terminal Packing: A Puzzle and a Paradox

Biman Bagchi

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Abstract

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?

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Biman Bagchi. 2026-08-30. From Freezing to Terminal Packing: A Puzzle and a Paradox. https://arxiv.org/abs/2608.29676

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