This study introduces the Disordered Enthalpy–Entropy Descriptor (DEED), a new descriptor that captures the balance between entropy gains and enthalpy costs in the formation of homogeneous solid solutions in high-entropy ceramics. DEED is designed to classify the functional synthesizability of multicomponent ceramics, regardless of their chemistry and structure. The descriptor is based on the thermodynamic density of states and considers both the entropic gain and enthalpy cost associated with the formation of disordered materials. To enable efficient calculations, the researchers developed a convolutional algorithm that drastically reduces computational resources. This algorithm, called convolutional POCC (cPOCC), allows for the approximation of the thermodynamic density of states for complex systems, enabling the calculation of DEED for a wide range of materials. The study demonstrates that DEED accurately predicts the functional synthesizability of high-entropy ceramics, including carbides, carbonitrides, and borides. The descriptor is validated through experimental results, showing that DEED correctly predicts the synthesizability of various materials, including new single-phase high-entropy carbonitrides and borides. The results indicate that DEED is a reliable tool for computational discovery of novel high-entropy ceramics. The study also highlights the importance of considering the process perspective in materials discovery, emphasizing the need for a descriptor that accounts for the relationship between synthesis conditions and material properties. DEED provides a framework for understanding the balance between entropy and enthalpy in the formation of disordered materials, enabling the prediction of functional synthesizability and guiding experimental discovery. Overall, the introduction of DEED represents a significant advancement in the field of high-entropy ceramics, offering a new approach to materials discovery that combines computational and experimental methods. The descriptor has the potential to accelerate the discovery of new materials with desirable properties for extreme environments.This study introduces the Disordered Enthalpy–Entropy Descriptor (DEED), a new descriptor that captures the balance between entropy gains and enthalpy costs in the formation of homogeneous solid solutions in high-entropy ceramics. DEED is designed to classify the functional synthesizability of multicomponent ceramics, regardless of their chemistry and structure. The descriptor is based on the thermodynamic density of states and considers both the entropic gain and enthalpy cost associated with the formation of disordered materials. To enable efficient calculations, the researchers developed a convolutional algorithm that drastically reduces computational resources. This algorithm, called convolutional POCC (cPOCC), allows for the approximation of the thermodynamic density of states for complex systems, enabling the calculation of DEED for a wide range of materials. The study demonstrates that DEED accurately predicts the functional synthesizability of high-entropy ceramics, including carbides, carbonitrides, and borides. The descriptor is validated through experimental results, showing that DEED correctly predicts the synthesizability of various materials, including new single-phase high-entropy carbonitrides and borides. The results indicate that DEED is a reliable tool for computational discovery of novel high-entropy ceramics. The study also highlights the importance of considering the process perspective in materials discovery, emphasizing the need for a descriptor that accounts for the relationship between synthesis conditions and material properties. DEED provides a framework for understanding the balance between entropy and enthalpy in the formation of disordered materials, enabling the prediction of functional synthesizability and guiding experimental discovery. Overall, the introduction of DEED represents a significant advancement in the field of high-entropy ceramics, offering a new approach to materials discovery that combines computational and experimental methods. The descriptor has the potential to accelerate the discovery of new materials with desirable properties for extreme environments.