发表机构
Washington University in St. Louis（华盛顿大学圣路易斯分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对冰I多型体，通过转移算子、Schatten-Hölder不等式等方法，证明交替六方堆叠的质子构型熵最大，并给出构型常数w的上下端点范围及立方冰对应w的上限。
AI 中文摘要
冰I存在立方、六方及混合层堆叠形式，但严格的熵比较研究多聚焦于两种理想端元。我们用非负转移算子K及其转置的字表示所有循环均匀配准堆叠；对每个此类偶长字，应用Schatten-Hölder不等式可证明，交替六方堆叠在所有常见有限截面下使冰规则计数最大化，因此在所有周期均匀配准多型体中构型常数最大。我们通过将Nagle的正偶子图展开限制于精确枚举的不交块得到下端点，利用Finner的二阶超图Hölder不等式及双副本棱镜转移算子的有理Collatz-Wielandt证书得到上端点。这些构造给出1.503360 ≤ w ≤ 1.540196，其中w(Ic) ≤ 1.527699。
英文摘要
Ice I admits cubic, hexagonal, and mixed layer stackings, but rigorous comparisons of its proton configurational entropy have focused on the two ideal endmembers. We identify every cyclic uniform-registry ice-I stacking with a word in a nonnegative layer-transfer operator and its transpose. Applying the Schatten-Hölder inequality to every even-length word proves that alternating hexagonal stacking maximizes the ice-rule configuration count at each common finite cross-section. Consequently, hexagonal ice maximizes the thermodynamic configuration constant among all periodic uniform-registry ice-I polytypes. We also construct rigorous lower and upper bounds without finite-size extrapolation. Restricting Nagle's positive even-subgraph expansion to disjoint blocks gives the lower bound; Finner's hypergraph Hölder inequality and rational Collatz-Wielandt certificates for two-replica prism operators give the upper bounds. The resulting configuration constant $w$, whose logarithm is the entropy per molecule in units of Boltzmann's constant, satisfies $1.503360 \le w \le 1.540196$, with the sharper cubic-ice ceiling $w \le 1.527699$. The same bracket controls lower and upper configuration growth rates of fixed aperiodic stackings along the specified prism-tileable exhaustions. These results establish hexagonal stacking as a possibly nonunique maximizer; equality of the cubic and hexagonal entropy constants remains unresolved.
Comments24 pages, 4 figures. Appendices A-G included
