Following up on our finding of a universal hidden order in tessellations with the Quantizer energy functionals (where the cells minimize the second moment of the volume distribution) using Lloyd’s algorithm, we now compared these states with quenches from equilibrium states at finite temperature.
T. M. Hain, M. A. Klatt, G. E. Schröder-Turk. Low-temperature statistical mechanics of the Quantizer problem: Fast quenching and equilibrium cooling of the three-dimensional Voronoi liquid. J. Chem. Phys. 153:234505-1–11 (2020).
Upon sufficiently fast non-equilibrium cooling, the system adopts similar states as the effectively hyperuniform inherent structures found by Lloyd’s algorithm and prevents the ordering transition into a body-centered cubic ordered structure.