  The slow down of dynamics in glass forming liquids as the glass transition is
approached has been characterised through the Adam-Gibbs relation, which
relates relaxation time scales to the configurational entropy. The Adam-Gibbs
relation cannot apply simultaneously to all relaxation times scales unless they
are coupled, and exhibit closely related temperature dependences. The breakdown
of the Stokes-Einstein relation presents an interesting situation to the
contrary, and in analysing it, it has recently been shown that the Adam-Gibbs
relation applies to diffusion coefficients rather than to viscosity or
structural relaxation times related to the decay of density fluctuations.
However, for multi-component liquids -- the typical cases considered in
computer simulations, metallic glass formers, etc. -- such a statement raises
the question of which diffusion coefficient is described by the Adam-Gibbs
relation. All diffusion coefficients can be consistently described by the
Adam-Gibbs relation if they bear a power law relationship with each other.
Remarkably, we find that for a wide range of glass formers, and for a wide
range of temperatures spanning the normal and the slow relaxation regimes, such
a relationship holds. We briefly discuss possible rationalisations of the
observed behaviour.
