2024/04/18 by V. M. Pergamenshchik, Pergamenshchik, V. M.
Engineering · Mathematics · #Advanced Statistical Methods and Models #FOS: Physical sciences #Mathematical Dynamics and Fractals #Phase Equilibria and Thermodynamics #Soft Condensed Matter (cond-mat.soft)
paper · pdf · doi:10.48550/arxiv.2404.12506
openalex publication_date 2024/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
The one-body free volume, which determines the entropy of a hard disk system, has extensive (cavity) and intensive (cell) contributions. So far these contributions have not been unified and considered separately. The presented theory incorporates both contributions, and their sum is shown to determine the free volume and partition function. The approach is based on multiple intersections of the circles concentric with the disks but of twice larger radius. The result is exact formulae for the extensive and intensive entropy contributions in terms of the intersections of just two, three, four, and five circles. The method has an important advantage for applications in numerical simulations: the formulae enable one to convert the disk coordinates into the entropy contribution directly without any additional geometric construction. The theory can be straightforwardly applied to a system of hard spheres.