  In recent years, the possibility of algorithmically preparing ultra-stable
glasses (UG), i.e., states that lie very deep in the potential energy
landscape, has considerably expanded our understanding of the glassy state. In
this work, we report on a new protocol for ultrastable glass preparation that
iteratively modifies the particle diameters to reduce local virial stress
fluctuations. We apply the algorithm to an additive Lennard-Jones mixture and
show that, compared to the states obtained via thermal annealing, virial
homogenized glasses (VHG) are characterized by a considerable increase in both
kinetic stability and the number of locally favored structures (icosahedra). We
also consider the melting dynamics during heating ramps and show that it occurs
via an accumulation of localized events. Our results highlight the connection
between the thermodynamic and mechanical stability of ultra-stable glassy
states.
