2024/10/29 by Edward Bormashenko, Bormashenko, Edward, Shraga Shoval +5
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Optical measurement and interference techniques #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2410.21668
openalex publication_date 2024/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Voronoi Entropy (VE) and the continuous measure of symmetry (CSM) characterize the orderliness of a set of points on a 2D plane. The Voronoi entropy is the Shannon entropy of the Voronoi tessellation of the plane into polygons, quantifying the diversity of polygons. The VE is widely used to study the self-assembly of colloidal, supramolecular, and other systems. The value of VE changes from S=0 for a completely ordered system, built of polygons with an equal number of sides, to S=1.690+/-0.001 for a random set of points. While the VE takes into account only neighboring polygons, covering the 2D plane imposes constraints on the number of polygons and the number of edges in polygons. Consequently, unlike the conventional Shannon Entropy, the VE captures some long-range order properties of the system. We calculate the VE for several hyperuniform sets of points and compare it with the values of exponents of collective density variables characterizing long-range correlations in the system. We show that the VE correlates with the latter up to a certain saturation level, after which the value of the VE falls to S=0, and we explain this phenomenon.