The lack of clarity of various mode-coupling theory (MCT) approximations,even in equilibrium,makes it hard to understand the relation between variousMCT approaches for sheared steady states as well as their regime of validity.Here we try to understand these approximations indirectly by deriving the MCTequations through two different approaches for a colloidal system under shear,first, through a microscopic approach, as suggested by Zaccarelli et al, andsecond, through fluctuating hydrodynamics, where the approximations used in thederivation are quite clear. The qualitative similarity of our theory with anumber of existing theories show that linear response theory might play a rolein various approximations employed in deriving those theories and one needs tobe careful while applying them for systems arbitrarily far away fromequilibrium, such as a granular system or when shear is very strong. As abyproduct of our calculation, we obtain the extension of Yvon-Born-Green (YBG)equation for a sheared system and under the assumption of random-phaseapproximation, the YBG equation yields the distorted structure factor that wasearlier obtained through different approaches.
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