  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.
