A Unified Thermodynamic Framework: From Equilibrium and Nonequilibrium to Zentropy, Cross Phenomena, and Applications for AI and AI Safety

Abstract

Thermodynamics is traditionally viewed as a theory of equilibrium because Gibbs formulated the combined law strictly for equilibrium systems. This historical limitation motivated the emergence of irreversible thermodynamics as a distinct field. Subsequent advances, including Kaufman’s introduction of lattice stability for quantitative treatment of nonequilibrium phases, Hillert’s integration of entropy production into the combined law, and Ågren’s development of the modern theory of atomic mobility, collectively extended Gibbs’s framework to describe real materials under evolving thermodynamic driving forces. The present author further refined Hillert’s nonequilibrium formalism by introducing partial internal energy, partial entropy, and partial volume for each component directly into the first, second, and combined laws. This refinement yields an explicit definition for the chemical potential in terms of these partial quantities, resolving subtle interdependencies among entropy, volume, and composition in open systems. Building on this foundation and Ågren’s mobility theory, the author developed and later revised the theory of cross phenomena, deriving transport equations from the first law and addressing limitations inherent in phenomenological Onsager formulations. In parallel, the author and collaborators established zentropy theory, which unifies quantum mechanics and Gibbs statistical mechanics to predict entropy and Helmholtz energy from a full ensemble of symmetry-broken configurations. This framework enables quantitative prediction of Helmholtz energy landscapes with basins, ridges, and apices across stable, metastable, and unstable states. Together, these developments establish a unified thermodynamic framework spanning equilibrium, nonequilibrium, statistical, and quantum descriptions across all-scales, and provide a thermodynamics-based artificial intelligence (AI) framework exemplified by the zentropy-enhanced neural network (ZENN), yielding physically grounded, interpretable predictions. This new AI framework also incorporates built-in safety mechanisms, including structural containment through configuration partitioning and dynamic containment via zentropy-based regulation of driving forces and system stability.