Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres

The residual multiparticle entropy (RMPE) of a fluid is defined as the difference, [Formula: see text] , between the excess entropy per particle (relative to an ideal gas with the same temperature and density), [Formula: see text] , and the pair-correlation contribution, [Formula: see text]. Thus, the RMPE represents the net contribution to [Formula: see text] 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 [Formula: see text] 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 [Formula: see text]. It is observed that, for any given dimensionality d, the RMPE takes negative values for small densities, reaches a negative minimum [Formula: see text] at a packing fraction [Formula: see text] , and then rapidly increases, becoming positive beyond a certain packing fraction [Formula: see text]. Interestingly, while both [Formula: see text] and [Formula: see text] monotonically decrease as dimensionality increases, the value of [Formula: see text] exhibits a nonmonotonic behavior, reaching an absolute minimum at a fractional dimensionality [Formula: see text]. A plot of the scaled RMPE [Formula: see text] shows a quasiuniversal behavior in the region [Formula: see text].