Hexagonal Stacking Maximizes Proton Configurational Entropy among Ice-I Polytypes
arXiv:2608.07613
Abstract
Ice I admits cubic, hexagonal, and mixed layer stackings, but rigorous entropy comparisons have focused on the two ideal endmembers. We represent every cyclic uniform-registry stacking by a word in a nonnegative transfer operator K and its transpose. For every such even-length word, applying the Schatten-Hölder inequality proves that alternating hexagonal stacking maximizes the ice-rule count at every common finite cross-section; the configuration constant is therefore maximal among all periodic uniform-registry polytypes. We obtain the lower endpoint by restricting Nagle's positive even-subgraph expansion to exactly enumerated disjoint blocks. Finner's degree-two hypergraph Hölder inequality and rational Collatz-Wielandt certificates for two-replica prism transfer operators give the upper endpoints. These constructions yield , with .
14 pages, 4 figures. Supplemental Material included as appendices S1-S7