  Non-equilibrium molecular dynamics simulations were performed to study the
thermodynamic, structural, and dynamical properties of the single-component
Lennard-Jones and the Kob-Andersen binary Lennard-Jones liquids. Both systems
are known to be strongly correlating, i.e., have strong correlations between
equilibrium thermal fluctuations of virial and potential energy. Such systems
have good isomorphs, i.e., curves in the thermodynamic phase diagram along
which structural, dynamical, and some thermodynamic quantities are invariant
when expressed in reduced units. The SLLOD equations of motion were used to
simulate Couette shear flows of the two systems. We show analytically that
these equations are isomorph invariant provided the reduced strain rate is
fixed along the isomorph. Since isomorph invariance is generally only
approximate, a range of shear rates were simulated to test for the predicted
invariance, covering both the linear and non-linear regimes. For both systems,
when represented in reduced units the radial distribution function and the
intermediate scattering function collapse for state points that are isomorphic.
The strain-rate dependence of the viscosity, which exhibits shear thinning, is
also invariant along an isomorph. Our results extend the isomorph concept to
the state-state non-equilibrium situation of a shear flow, in which the phase
diagram is three dimensional because the shear rate defines the third
dimension.
