Approach to the non-equilibrium time-periodic state in a 'steady' shear flow model

The standard non-equilibrium molecular dynamics algorithm for steady shear flow (SLLOD) employs Lees-Edwards periodic boundary conditions. It is not widely known that these boundary conditions make the system non-autonomous. The 'steady state' shear stress is in fact time periodic. The standard response theory derivations for steady shear do not take proper account of these non-autonomous terms. In this paper we correct this deficiency. We show that these non-autonomous terms invalidate the Green-Kubo relation for the finite frequency shear viscosity of fluids under Lees-Edwards periodic boundary conditions.