  In modeling nonequilibrium systems one usually starts with a definition of
the microscopic dynamics, e.g., in terms of transition rates, and then derives
the resulting macroscopic behavior. We address the inverse question for a class
of steady state systems, namely complex fluids under continuous shear flow: how
does an externally imposed shear current affect the microscopic dynamics of the
fluid? The answer can be formulated in the form of invariant quantities, exact
relations for the transition rates in the nonequilibrium steady state, as
discussed in a recent letter [A. Baule and R. M. L. Evans, Phys. Rev. Lett.
101, 240601 (2008)]. Here, we present a more pedagogical account of the
invariant quantities and the theory underlying them, known as the
nonequilibrium counterpart to detailed balance (NCDB). Furthermore, we
investigate the relationship between the transition rates and the shear current
in the steady state. We show that a fluctuation relation of the
Gallavotti-Cohen type holds for systems satisfying NCDB.
