  The Adam-Gibbs (AG) relation connects the dynamics of a glass-forming liquid
to its the thermodynamics via. the configurational entropy, and is of
fundamental importance in descriptions of glassy behaviour. The breakdown of
the Stokes-Einstein (SEB) relation between the diffusion coefficient and the
viscosity (or structural relaxation times) in glass formers raises the question
as to which dynamical quantity the AG relation describes. By performing
molecular dynamics simulations, we show that the AG relation is valid over the
widest temperature range for the diffusion coefficient and not for the
viscosity or relaxation times. Studying relaxation times defined at a given
wavelength, we find that SEB and the deviation from the AG relation occur below
a temperature at which the correlation length of dynamical heterogeneity equals
the wavelength probed.

Statistical Mechanics