  Intermolecular correlations lower values of both diffusion and entropy. We
present an analysis of the existing relations between long-time diffusion (D)
and entropy. S. A recently proposed inequality, a lower bound, by Sorkin et
al., expresses the long-time diffusion in terms of diffusion in a reference
state and the entropy difference. Such a relationship may provide a measure of
intermolecular correlations. We show that for a one-dimensional rugged energy
landscape, the lower bound becomes equality only if certain three-site
correlations are neglected. When these correlations are included, we can derive
an accurate expression that agrees with computer simulations. The strong
dimensionality dependence of diffusion of a Brownian particle in a rugged
energy landscape also resembles the recently proposed inequality. We show that
for interacting colloids, a mode-coupling theory-type calculation of diffusion
coefficient can be combined with the new inequality to estimate entropy change
from long-range inter-colloid correlations. Interestingly, the rate of barrier
crossing in a multidimensional potential energy surface, related to diffusion
in a periodic lattice, is shown to admit a relation that depends on the entropy
change in a way reminiscent of the relation between D and S.
