Finite-size excess-entropy scaling for simple liquids

TL;DR

This paper introduces a finite-size scaling approach for excess entropy in simple liquids, demonstrating how it affects self-diffusivity and revealing a potential constant viscosity to entropy ratio.

Contribution

It develops and validates a finite-size excess entropy integral equation, linking system size effects to diffusivity and viscosity in simple liquids.

Findings

Excess entropy $s_2$ scales with inverse system size.

Self-diffusivity $D^*$ exhibits similar finite-size effects.

A power law relates scaling coefficients for $D^*$ and $s_2$.

Abstract

We introduce and validate a finite-size two-body excess entropy integral equation. By using analytical arguments and computer simulations of prototypical simple liquids, we show that the excess entropy $s_2$ exhibits a finite-size scaling with the inverse of the linear size of the simulation box. Since the self-diffusivity coefficient $D^*$ displays a similar finite-size effect, we show that the scaling entropy relation $D^*=A\exp(\alpha s_2)$ also depends on the simulation box size. By extrapolating to the thermodynamic limit, we report values for the coefficients $A$ and $\alpha$ that agree well with values available in the literature. Finally, we find a power law relation between the scaling coefficients for $D^*$ and $s_2$, suggesting a constant viscosity to entropy ratio.