Revisiting the Stokes-Einstein relation without a hydrodynamic diameter.

We present diffusion coefficient and shear viscosity data for the Lennard-Jones fluid along nine isochores above the critical density, each involving a temperature variation of roughly two orders of magnitude. The data are analyzed with respect to the Stokes-Einstein (SE) relation, which breaks down gradually at high temperatures. This is rationalized in terms of the fact that the reduced diffusion coefficient D ̃ and the reduced viscosity η ̃ are both constant along the system's lines of constant excess entropy (the isomorphs). As a consequence, D ̃ η ̃ is a function of T/T Ref(ρ) in which T is the temperature, ρ is the density, and T Ref(ρ) is the temperature as a function of the density along a reference isomorph. This allows one to successfully predict the viscosity from the diffusion coefficient in the studied region of the thermodynamic phase diagram.