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(ex), and the pair-correlation contribution, s(2). 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.; Lopez 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 phi. It is observed that, for any given dimensionality d, the RMPE takes negative values for small densities, reaches a negative minimum Delta s(min) at a packing fraction phi(min), and then rapidly increases, becoming positive beyond a certain packing fraction phi(0). Interestingly, while both fmin and phi(0) monotonically decrease as dimensionality increases, the value of Delta s(min) exhibits a nonmonotonic behavior, reaching an absolute minimum at a fractional dimensionality d similar or equal to 2.38. A plot of the scaled RMPE Delta s/vertical bar Delta s(min)vertical bar shows a quasiuniversal behavior in the region -0.14 less than or similar to phi - phi(0) less than or similar to 0.02.