Incorporation of the intensive and extensive entropy contributions in the disk intersection theory of a hard disk system
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 determi...
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| Format: | Article |
| Language: | English |
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Institute for Condensed Matter Physics
2023-07-01
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| Series: | Condensed Matter Physics |
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| Online Access: | https://doi.org/10.5488/CMP.26.33501 |
| _version_ | 1797752207297216512 |
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| author | V. M. Pergamenshchik |
| author_facet | V. M. Pergamenshchik |
| author_sort | V. M. Pergamenshchik |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T17:00:57Z |
| format | Article |
| id | doaj.art-83daf518e5434326adcb230dd9ea91fe |
| institution | Directory Open Access Journal |
| issn | 1607-324X 2224-9079 |
| language | English |
| last_indexed | 2024-03-12T17:00:57Z |
| publishDate | 2023-07-01 |
| publisher | Institute for Condensed Matter Physics |
| record_format | Article |
| series | Condensed Matter Physics |
| spelling | doaj.art-83daf518e5434326adcb230dd9ea91fe2023-08-07T13:38:58ZengInstitute for Condensed Matter PhysicsCondensed Matter Physics1607-324X2224-90792023-07-012633350110.5488/CMP.26.33501Incorporation of the intensive and extensive entropy contributions in the disk intersection theory of a hard disk systemV. M. PergamenshchikThe 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.https://doi.org/10.5488/CMP.26.33501hard discsfree volumepartition functionintersections |
| spellingShingle | V. M. Pergamenshchik Incorporation of the intensive and extensive entropy contributions in the disk intersection theory of a hard disk system Condensed Matter Physics hard discs free volume partition function intersections |
| title | Incorporation of the intensive and extensive entropy contributions in the disk intersection theory of a hard disk system |
| title_full | Incorporation of the intensive and extensive entropy contributions in the disk intersection theory of a hard disk system |
| title_fullStr | Incorporation of the intensive and extensive entropy contributions in the disk intersection theory of a hard disk system |
| title_full_unstemmed | Incorporation of the intensive and extensive entropy contributions in the disk intersection theory of a hard disk system |
| title_short | Incorporation of the intensive and extensive entropy contributions in the disk intersection theory of a hard disk system |
| title_sort | incorporation of the intensive and extensive entropy contributions in the disk intersection theory of a hard disk system |
| topic | hard discs free volume partition function intersections |
| url | https://doi.org/10.5488/CMP.26.33501 |
| work_keys_str_mv | AT vmpergamenshchik incorporationoftheintensiveandextensiveentropycontributionsinthediskintersectiontheoryofaharddisksystem |