Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres   The residual multiparticle entropy (RMPE) of a fluid is defined as the
difference, $\Delta s$, between the excess entropy per particle (relative to an
ideal gas with the same temperature and density), $s_\text{ex}$, and the
pair-correlation contribution, $s_2$. Thus, the RMPE represents the net
contribution to $s_\text{ex}$ 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.; L\'opez de Haro, M. \emph{Phys. Rev. E} \textbf{2016}, \emph{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 $\phi$. It is observed that, for any given
dimensionality $d$, the RMPE takes negative values for small densities, reaches
a negative minimum $\Delta s_{\text{min}}$ at a packing fraction
$\phi_{\text{min}}$, and then rapidly increases, becoming positive beyond a
certain packing fraction $\phi_0$. Interestingly, while both
$\phi_{\text{min}}$ and $\phi_0$ monotonically decrease as dimensionality
increases, the value of $\Delta s_{\text{min}}$ exhibits a nonmonotonic
behavior, reaching an absolute minimum at a fractional dimensionality $d\simeq
2.38$. A plot of the scaled RMPE $\Delta s/|\Delta s_{\text{min}}|$ shows a
quasiuniversal behavior in the region $-0.14\lesssim\phi-\phi_0\lesssim 0.02$.

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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: math
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom