Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres
The residual multiparticle entropy (RMPE) of a fluid is defined as the difference, Δs, between the excess entropy per particle (relative to an ideal gas with the same temperature and density), sex, and the pair-correlation contribution, s2. Thus, the RMPE represents the net contribution to...
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MDPI AG
2018-07-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/20/7/544 |
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| author | Andrés Santos Franz Saija Paolo V. Giaquinta |
| author_facet | Andrés Santos Franz Saija Paolo V. Giaquinta |
| author_sort | Andrés Santos |
| collection | DOAJ |
| description | The residual multiparticle entropy (RMPE) of a fluid is defined as the difference, Δs, between the excess entropy per particle (relative to an ideal gas with the same temperature and density), sex, and the pair-correlation contribution, s2. Thus, the RMPE represents the net contribution to sex due to spatial correlations involving three, four, or more particles. A heuristic “ordering” criterion identifies the vanishing of the RMPE as an underlying signature of an impending structural or thermodynamic transition of the system from a less ordered to a more spatially organized condition (freezing is a typical example). Regardless of this, the knowledge of the RMPE is important to assess the impact of non-pair multiparticle correlations on the entropy of the fluid. Recently, an accurate and simple proposal for the thermodynamic and structural properties of a hard-sphere fluid in fractional dimension 1<d<3 has been proposed (Santos, A.; López de Haro, M. Phys. Rev. E 2016, 93, 062126). The aim of this work is to use this approach to evaluate the RMPE as a function of both d and the packing fraction ϕ. It is observed that, for any given dimensionality d, the RMPE takes negative values for small densities, reaches a negative minimum Δsmin at a packing fraction ϕmin, and then rapidly increases, becoming positive beyond a certain packing fraction ϕ0. Interestingly, while both ϕmin and ϕ0 monotonically decrease as dimensionality increases, the value of Δsmin exhibits a nonmonotonic behavior, reaching an absolute minimum at a fractional dimensionality d≃2.38. A plot of the scaled RMPE Δs/|Δsmin| shows a quasiuniversal behavior in the region −0.14≲ϕ−ϕ0≲0.02. |
| first_indexed | 2024-04-13T08:17:27Z |
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| id | doaj.art-ed047a51d3ee41859aa5a961d714568c |
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| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-13T08:17:27Z |
| publishDate | 2018-07-01 |
| publisher | MDPI AG |
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| series | Entropy |
| spelling | doaj.art-ed047a51d3ee41859aa5a961d714568c2022-12-22T02:54:44ZengMDPI AGEntropy1099-43002018-07-0120754410.3390/e20070544e20070544Residual Multiparticle Entropy for a Fractal Fluid of Hard SpheresAndrés Santos0Franz Saija1Paolo V. Giaquinta2Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006 Badajoz, SpainCNR-IPCF, Viale F. Stagno d’Alcontres, 37-98158 Messina, ItalyDipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Contrada Papardo, 98166 Messina, ItalyThe residual multiparticle entropy (RMPE) of a fluid is defined as the difference, Δs, between the excess entropy per particle (relative to an ideal gas with the same temperature and density), sex, and the pair-correlation contribution, s2. Thus, the RMPE represents the net contribution to sex due to spatial correlations involving three, four, or more particles. A heuristic “ordering” criterion identifies the vanishing of the RMPE as an underlying signature of an impending structural or thermodynamic transition of the system from a less ordered to a more spatially organized condition (freezing is a typical example). Regardless of this, the knowledge of the RMPE is important to assess the impact of non-pair multiparticle correlations on the entropy of the fluid. Recently, an accurate and simple proposal for the thermodynamic and structural properties of a hard-sphere fluid in fractional dimension 1<d<3 has been proposed (Santos, A.; López de Haro, M. Phys. Rev. E 2016, 93, 062126). The aim of this work is to use this approach to evaluate the RMPE as a function of both d and the packing fraction ϕ. It is observed that, for any given dimensionality d, the RMPE takes negative values for small densities, reaches a negative minimum Δsmin at a packing fraction ϕmin, and then rapidly increases, becoming positive beyond a certain packing fraction ϕ0. Interestingly, while both ϕmin and ϕ0 monotonically decrease as dimensionality increases, the value of Δsmin exhibits a nonmonotonic behavior, reaching an absolute minimum at a fractional dimensionality d≃2.38. A plot of the scaled RMPE Δs/|Δsmin| shows a quasiuniversal behavior in the region −0.14≲ϕ−ϕ0≲0.02.http://www.mdpi.com/1099-4300/20/7/544residual multiparticle entropyhard spheresfractal dimension |
| spellingShingle | Andrés Santos Franz Saija Paolo V. Giaquinta Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres Entropy residual multiparticle entropy hard spheres fractal dimension |
| title | Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres |
| title_full | Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres |
| title_fullStr | Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres |
| title_full_unstemmed | Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres |
| title_short | Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres |
| title_sort | residual multiparticle entropy for a fractal fluid of hard spheres |
| topic | residual multiparticle entropy hard spheres fractal dimension |
| url | http://www.mdpi.com/1099-4300/20/7/544 |
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