Abstract: High-entropy ceramics (HECs) demonstrate exceptional thermal and mechanical properties, along with outstanding chemical stability, which can be attributed to their high entropy, lattice distortion, sluggish diffusion, and cocktail effects. However, the expansive compositional and structural space associated with HEC renders traditional trial-and-error methods time-consuming, costly, and inadequate for the investigation of complex systems. Thus, theoretical calculation has become an indispensable tool for addressing these challenges. To outline recent advances in theoretical calculation for HEC, this article focuses on prevalent calculation methods, including first-principles calculations, molecular dynamics, machine learning, and calculation of phase diagrams. Additionally, it discusses research paradigms such as high-throughput computing and performance descriptors, providing a comprehensive overview of their key roles and specific applications in HEC. The article first outlines the fundamental characteristics and core effects of HEC, then turns to critically examine the theoretical basis of these calculation methods, elaborating on their applications through specific examples in composition design, property prediction, microstructural parsing, and phase stability assessment. Finally, this paper summarizes the major challenges encountered in theoretical calculations in the study of multi-component systems, such as the scarcity of high-quality datasets and the ambiguity of structure-property relationships. It concludes with a forward-looking outlook on the directions in this field, including data-driven design, cross-scale correlation, and extreme environment simulation.

Key words: high-entropy ceramic, theoretical calculation, first principles, multiscale simulation, machine learning, review