Article
Version 1
Preserved in Portico This version is not peer-reviewed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.
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/|Δsmin| shows a quasiuniversal behavior in the region −0.14 ≲ ϕ − ϕ0 ≲ 0.02.
Keywords
residual multiparticle entropy; hard spheres; fractal dimension
Subject
Physical Sciences, Condensed Matter Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment