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Open AccessArticle

Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres

Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006 Badajoz, Spain
CNR-IPCF, Viale F. Stagno d’Alcontres, 37-98158 Messina, Italy
Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Contrada Papardo, 98166 Messina, Italy
Author to whom correspondence should be addressed.
Entropy 2018, 20(7), 544;
Received: 1 July 2018 / Revised: 18 July 2018 / Accepted: 20 July 2018 / Published: 23 July 2018
(This article belongs to the Special Issue Entropy: From Physics to Information Sciences and Geometry)
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 d2.38. A plot of the scaled RMPE Δs/|Δsmin| shows a quasiuniversal behavior in the region 0.14ϕϕ00.02. View Full-Text
Keywords: residual multiparticle entropy; hard spheres; fractal dimension residual multiparticle entropy; hard spheres; fractal dimension
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Santos, A.; Saija, F.; Giaquinta, P.V. Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres. Entropy 2018, 20, 544.

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