Emerging quasi-0D states at vanishing total entropy of the 1D hard sphere system: A coarse-grained similarity to the car parking problem

• Published in: Physics letters. A Vol. 378; no. 26-27; pp. 1780 - 1786
• Main Author: Frusawa, Hiroshi
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 16.05.2014
• Subjects: Car parking; Car parking problem; Crossovers; Density; Emergence; Entropy; Hard sphere; Heterogeneity; High speed tool steels; One-dimensional system; Similarity; One-dimensional system; Car parking problem; Hard sphere
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2014.04.066

A coarse-grained system of one-dimensional (1D) hard spheres (HSs) is created using the Delaunay tessellation, which enables one to define the quasi-0D state. It is found from comparing the quasi-0D and 1D free energy densities that a frozen state due to the emergence of quasi-0D HSs is thermodynamically more favorable than fluidity with a large-scale heterogeneity above crossover volume fraction of ϕc=e/(1+e)=0.731⋯ , at which the total entropy of the 1D state vanishes. The Delaunay-based lattice mapping further provides a similarity between the dense HS system above ϕc and the jamming limit in the car parking problem. •A simple free energy form of quasi-0D hard spheres embedded in the 1D systems is obtained.•The quasi-0D state is thermodynamically more favorable than inhomogeneous fluidity above the volume fraction of about 73%.•The Delaunay tessellation provides a coarse-grained similarity to the jamming limit in the car parking problem.