The disordered and defect-rich structure of amorphous solids forms heterogeneous, high-dimensional energy landscapes. Thermally activated dynamics in such an energy landscape can be described by a discrete-state network of transitions between stable energy minima. Under low-frequency mechanical oscillations, the ensemble of transitions can come in resonance with a mechanical wave and provide a microscopic mechanism for mechanical dissipation. Traditionally, this dissipation is modeled by a superposition of independent two-level systems (TLS). Using molecular simulations, we find spatially correlated and strongly interacting transitions that form a sparsely connected network with complex topologies. Based on this observation, we develop an analytically tractable theory for mechanical loss of the full network from a nonequilibrium thermodynamic perspective. Our theory can be viewed as a rigorous generalization of the 50 year old single TLS model that explains many universal low temperature properties of disordered solids. An annealing study combined with an analysis of dominant relaxation paths in the energy landscape reveals novel mechanisms for reducing room temperature mechanical loss in this connected network perspective.
[1] S. Blaber, D. Bruns, J. Rottler, Proc. Natl. Acad. Sci. U.S.A., 123, e2513161123 (2026)
[2] Steven Blaber, Jörg Rottler, arXiv:2607.17434