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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{bagchi2026from,
  title = {{From Freezing to Terminal Packing: A Puzzle and a Paradox}},
  author = {Biman Bagchi},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29676},
  eprint = {2608.29676},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29676},
}
RIS
TY  - UNPB
TI  - From Freezing to Terminal Packing: A Puzzle and a Paradox
AU  - Biman Bagchi
PY  - 2026
DA  - 2026/08/30
PB  - arXiv
DO  - 10.48550/arxiv.2608.29676
UR  - https://arxiv.org/abs/2608.29676
AB  - 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?
ER  -