Excess entropy determines the applicability of Stokes-Einstein relation in simple fluids

The Stokes-Einstein (SE) relation between the self-diffusion and shear viscosity coefficients operates in sufficiently dense liquids not too far from the liquid-solid phase transition. By considering four simple model systems with very different pairwise interaction potentials (Lennard-Jones, Coulomb, Debye-H\"uckel or screened Coulomb, and the hard sphere limit) we identify where exactly on the respective phase diagrams the SE relation holds. It appears that the reduced excess entropy $s_{\rm ex}$ can be used as a suitable indicator of the validity of the SE relation. In all cases considered the onset of SE relation validity occurs at approximately $s_{\rm ex}\lesssim -2$. In addition, we demonstrate that the line separating gas-like and liquid-like fluid behaviours on the phase diagram is roughly characterized by $s_{\rm ex}\simeq -1$.