AbstractThe concept of quasi-particles forms the theoretical basis of our microscopic understanding of emergent phenomena associated with quantum-mechanical many-body interactions. However, the quasi-particle theory in disordered materials has proven difficult, resulting in the predominance of mean-field solutions. Here, we report first-principles phonon calculations and inelastic X-ray and neutron-scattering measurements on equiatomic alloys (NiCo, NiFe, AgPd, and NiFeCo) with force-constant dominant disorder—confronting a key 50-year-old assumption in the Hamiltonian of all mean-field quasi-particle solutions for off-diagonal disorder. Our results have revealed the presence of a large, and heretofore unrecognized, impact of local chemical environments on the distribution of the species-pair-resolved force-constant disorder that can dominate phonon scattering. This discovery not only identifies a critical analysis issue that has broad implications for other elementary excitations, such as magnons and skyrmions in magnetic alloys, but also provides an important tool for the design of materials with ultralow thermal conductivities.