  We analyze one thousand independent equilibrium trajectories of a system of
155 Lennard Jones particles to separate in a model-free approach the role of
temperature and the role of the explored potential energy landscape basin depth
in the particle dynamics. We show that the diffusion coefficient $D$ can be
estimated as a sum over over contributions of the sampled basins, establishing
a connection between thermodynamics and dynamics in the potential energy
landscape framework. We provide evidence that the observed non-linearity in the
relation between local diffusion and basin depth is responsible for the
peculiar dynamic behavior observed in supercooled states and provide an
interpretation for the presence of dynamic heterogeneities.
