Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres.

Abstract

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