Understanding phase stability and navigating vast compositional spaces in multicomponent solids remain central challenges in solid-state chemistry. Here, we develop a quantum spectral thermodynamic framework connecting interaction-induced phonon spectral broadening to free energy, alongside an uncertainty-guided active-learning workflow that explores 7.7 million high-entropy ceramic configurations at density-functional-theory fidelity, achieving a 10⁵-fold acceleration. We show that phonon self-energy effects arising from chemical disorder provide an intrinsic vibrational contribution to thermodynamic stabilization beyond ideal configurational entropy, compensating unfavorable mixing enthalpies and suppressing phase separation. Across the chemical space, we uncover a robust ~12 at.% solute threshold separating strengthening and softening regimes, associated with the filling of metal-carbon antibonding states. Chemical disorder further enables an unusual combination of high-temperature mechanical stiffness and low thermal conductivity, together with anomalous temperature-dependent lattice heat transport. This work establishes a quantum spectral foundation for connecting many-body interactions to thermodynamics and phase stability, while providing a scalable framework for exploring previously inaccessible multicomponent chemical spaces.