Nature, 381, 137 - 139 (1996) .

The author inadvertently omitted to mention an earlier result1 relating diffusion D, excess entropy s, density ρ and temperature T in liquids as D ρ1/3(m/kBT)1/2 = AeBs. It was interpreted2 as a convenient approximation of an essentially algebraic relation with B changing from 0.65 for hard spheres to 0.8 for soft spheres, and A varying within 30%.

The diffusion model presented in this Letter is conceptually distinct from these earlier results in recognizing that (1) liquid dynamics is controlled by the Enskog collisional mechanism, and (2) the rate of structural relaxation is proportional to the phase-space volume, that is, ∝es. This leads to D = C σ2Γes, where σ is the atomic diameter, Γ is the collision frequency and C is a universal constant; (1) is corroborated by the finding3 that the Kolmogorov–Sinai entropy in liquids, scaled by Γ, is universally related to s. In contrast to the timescale used in ref. 1, Γ is explicitly structure dependent; therefore, the variations of parameters in ref. 1 can be explained by non-universality of liquid structures. This Letter uses two-particle approximation of s, but a comprehensive test for full s was reported4.

An advantage of this relation involving no adjustable parameters is that it makes it possible to test unambiguously the diffusion model it quantifies. Besides liquids, this model holds for solid ionic conductors and quasicrystals. On the other hand, the relation can be used to detect a dynamical transition in supercooled liquids5.