Thermodynamics-governed integration of AI and ICME for materials design: Free-energy landscape and hierarchical entropy

Artificial intelligence (AI) and Integrated Computational Materials Engineering (ICME) are transforming materials design, yet their integration lacks a unifying physical foundation. Here, we propose a thermodynamics-governed framework centered on the free-energy landscape and the hierarchical (recursive) structure of entropy. By decomposing entropy into configurational and intrinsic contributions, materials behavior can be described consistently across all-scales within a single ensemble under given external constraints. Within this framework, ICME constructs physically grounded free-energy landscapes, while AI enables efficient learning and exploration of these landscapes. Applications to magnesium alloys illustrate how diverse phenomena emerge from a common thermodynamic foundation. This perspective shifts materials design from property-centered modeling to energy-centered, hierarchy-aware representations, providing a principled pathway for integrating AI and ICME.