Preprint Article Version 1 This version is not peer-reviewed

Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres

Version 1 : Received: 1 July 2018 / Approved: 3 July 2018 / Online: 3 July 2018 (13:07:09 CEST)

A peer-reviewed article of this Preprint also exists.

Santos, A.; Saija, F.; Giaquinta, P.V. Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres. Entropy 2018, 20, 544. Santos, A.; Saija, F.; Giaquinta, P.V. Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres. Entropy 2018, 20, 544.

Journal reference: Entropy 2018, 20, 544
DOI: 10.3390/e20070544

Abstract

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/smin| shows a quasiuniversal behavior in the region −0.14 ≲ ϕϕ0 ≲ 0.02.

Subject Areas

residual multiparticle entropy; hard spheres; fractal dimension

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