  A major challenge in simulating glassy systems is the ability to generate
configurations that may be found in equilibrium at sufficiently low
temperatures, in order to probe static and dynamic behaviour close to the glass
transition. A variety of approaches have recently explored ways of surmounting
this obstacle. Here, we explore the possibility of employing mechanical
agitation, in the form of cyclic shear deformation, to generate low energy
configurations in a model glass former. We perform shear deformation
simulations over a range of temperatures, shear rates and strain amplitudes. We
find that shear deformation induces faster relaxation towards low energy
configurations, or overaging, in simulations at sufficiently low temperatures,
consistently with previous results for athermal shear. However, for
temperatures at which simulations can be run till a steady state is reached
with or without shear deformation, we find that the inclusion of shear
deformation does not result in any speed up of the relaxation towards low
energy configurations. Although we find the configurations from shear
simulations to have properties indistinguishable from an equilibrium ensemble,
the cyclic shear procedure does not guarantee that we generate an equilibrium
ensemble at a desired temperature. In order to ensure equilibrium sampling, we
develop a hybrid Monte Carlo algorithm that employs cyclic shear as a trial
generation step, and has acceptance probabilities that depend not only on the
change in internal energy but also on heat dissipated (equivalently, work
done). We show that such an algorithm indeed generates an equilibrium ensemble.
