  Understanding the yielding of glass-forming systems upon shearing is
notoriously difficult since it is a strong non-equilibrium effect. Here we show
that the concept of the potential energy landscape (PEL), developed for the
quiescent state, can be extended to shearing. When introducing an appropriate
coarse graining of the extended PEL for sheared systems, one can distinguish
two fundamentally different types of plastic events, namely inherent structures
(IS) vs. minimized structure (MS) transitions. We apply these concepts to
non-cyclic and cyclic shearing of small systems, which allow us to characterize
the properties of elementary plastic events. Whereas the general properties of
the stress-strain curves are similar to larger systems, a closer analysis
reveals significantly different properties. This allows one to identify the
impact of the elastic coupling in larger systems. The concept of MS enables us
to relate the stress overshoot of a single trajectory to the emergence of an MS
transition. Furthermore, the occurrence of limit cycles can be characterized in
great detail for the small systems and connections to the properties of the PEL
can be formulated. Possible implications of our small-system results for the
macroscopic limit are discussed.
