Finite-size excess-entropy scaling for simple liquids

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 $D^{\ast }$ displays a similar finite-size effect, we show that the scaling entropy relation $D^{\ast }=A\exp (\alpha s_2)$ 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 $D^{\ast }$ and $s_2$, suggesting a constant viscosity to entropy ratio.