  Mechanical loss in amorphous solids at low frequencies is commonly attributed
to thermally activated transitions of isolated two-level systems (TLS) that
come in resonance with a mechanical wave. Using atomistic modeling of amorphous
silicon, we observe instead that the inherent structures that constitute the
TLS form a sparsely connected network with thermodynamic pathways between
states. An analytically tractable theory for mechanical loss of the full
network is derived from a nonequilibrium thermodynamic perspective. We show
that the connected network model predicts mechanical loss with distinct
temperature and frequency profiles when compared to the isolated TLS model.
This not only calls into question the validity of the TLS model, but also gives
us many new avenues and properties to analyze for the targeted design of low
mechanical loss materials for applications in gravitational wave detectors.
