Computational Discovery of Ultralow Thermal Conductivity in the Energy-Degenerate Polymorphic Crystal Family <b>A</b> _<b>2</b> <b>M</b> _<b>2</b> <b>M</b> ’ <b>Q</b> _<b>4</b>

Crystalline materials, characterized by their well-defined lattices, typically exhibit a unique global thermodynamic minimum for a specific composition. However, in this study, we discover a quaternary chalcogenide family, A₂M₂M'Q₄ (A: alkali metals; M: coinage metal; M': transition or group-IVA metals; Q: chalcogens), that exhibits pervasive energy (near-)degeneracy. For a given composition, multiple structurally distinct polymorphs exist within a formation enthalpy window of only a few milli-electron volts per atom. We quantify this inherent structural flexibility using a dedicated descriptor, σ_f: the standard deviation of formation enthalpies among degenerate (meta)stable polymorphs. The consistently low σ_f observed across the A₂M₂M'Q₄ family signifies a characteristically shallow and frustrated potential energy landscape, which drives pronounced lattice anharmonicity, marking these materials as prime candidates for ultralow lattice thermal conductivity (κ_L). Employing an advanced high-throughput computational framework that integrates thermodynamics, lattice dynamics, and thermal conductivity calculations, we screen 1215 A₂M₂M'Q₄ compounds, identifying 30 stable candidates with κ_L < 0.5 W m^-1 K^-1 at 300 K. Among them, Rb₂Ag₂SnTe₄ and Rb₂Au₂HfTe₄, two representatives from the IVA and TM subgroups, are predicted to show ultralow room-temperature κ_L of 0.174 W m^-1 K^-1 and 0.295 W m^-1 K^-1, respectively. A systematic analysis suggests that the nonbonding and antibonding states induced by "dual rattlers" are the origin of low thermal conductivity in these compounds. Our results position the A₂M₂M'Q₄ family as a rich source of intrinsic thermal insulators and suggest that polymorphic energy degeneracy may serve as a valuable signpost for identifying crystalline families with potential anharmonicity.