  Starting from the microscopic Smoluchowski equation for interacting Brownian
particles under stationary shearing, exact expressions for shear-dependent
steady-state averages, correlation and structure functions, and
susceptibilities are obtained, which take the form of generalized Green-Kubo
relations. They require integration of transient dynamics. Equations of motion
with memory effects for transient density fluctuation functions are derived
from the same microscopic starting point. We argue that the derived formal
expressions provide useful starting points for approximations in order to
describe the stationary non-equilibrium state of steadily sheared dense
colloidal dispersions.

Soft Condensed Matter;Statistical Mechanics