  Stokes-Einstein (SE) relation, which relates diffusion constant with the
viscosity of a liquid at high temperatures in equilibrium, is violated in the
supercooled temperature regime. Whether this relation is obeyed in
nonequilibrium active liquids is a question of significant current interest to
the statistical physics community trying to develop the theoretical framework
of nonequilibrium statistical mechanics. Via extensive computer simulations of
model active glass-forming liquids in three dimensions, we show that SE is
obeyed at a high temperature similar to the equilibrium behaviour, and it gets
violated in the supercooled temperature regimes. The degree of violation
increases systematically with the increasing activity which quantifies the
amount the system is driven out of equilibrium. First passage-time (FPT)
distributions helped us to gain insights into this enhanced breakdown from the
increased short-time peak, depicting hoppers. Subsequently, we study the wave
vector dependence of SE relation and show that it gets restored at a wave
vector that decreases with increasing activity, and the cross-over wave vector
is found to be proportional to the inverse of the dynamical heterogeneity
length scale in the system. Our work showed how SE violation in active
supercooled liquids could be rationalized using the growth of dynamic length
scale, which is found to grow enormously with increasing activity in these
systems.
