Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres.

The residual multiparticle entropy (RMPE) of a fluid is defined as the difference, Δ s , between the excess entropy per particle (relative to an ideal gas with the same temperature and density), s ex , and the pair-correlation contribution, s 2 . Thus, the RMPE represents the net contribution to s 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.; López de Haro, M. <italic>Phys. Rev. E</italic><bold>2016</bold>, <italic>93</italic>, 062126). The aim of this work is to use this approach to evaluate the RMPE as a function of both <italic>d</italic> and the packing fraction ϕ. It is observed that, for any given dimensionality <italic>d</italic>, the RMPE takes negative values for small densities, reaches a negative minimum Δ s min at a packing fraction ϕ min , and then rapidly increases, becoming positive beyond a certain packing fraction ϕ 0 . Interestingly, while both ϕ min and ϕ 0 monotonically decrease as dimensionality increases, the value of Δ s min exhibits a nonmonotonic behavior, reaching an absolute minimum at a fractional dimensionality d ≃ 2.38 . A plot of the scaled RMPE Δ s / | Δ s min | shows a quasiuniversal behavior in the region − 0.14 ≲ ϕ − ϕ 0 ≲ 0.02 . [ABSTRACT FROM AUTHOR]