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

Length-scale Dependence of Stokes-Einstien Breakdown in Active Glass-forming Liquids