  The interplay between structure and dynamics in non-equilibrium steady-state
is far from understood. We address this interplay by tracking Brownian Dynamics
trajectories of particles in a binary colloid of opposite charges in an
external electric field, undergoing cross-over from homogeneous to lane state,
a prototype of heterogeneous structure formation in non-equilibrium systems. We
show that the length scale of structural correlations controls heterogeneity in
diffusion and consequent anomalous dynamic responses, like the exponential tail
in probability distributions of particle displacements and stretched
exponential structural relaxation. We generalise our observations using
equations for steady state density which may aid to understand microscopic
basis of heterogeneous diffusion in condensed matter systems.
