Thermodynamics and its prediction and CALPHAD modeling: Review, state of the art, and perspectives

Thermodynamics is a science concerning the state of a system, whether it is stable, metastable, or unstable. The combined law of thermodynamics derived by Gibbs about 150 years ago laid the foundation of thermodynamics. In Gibbs combined law, the entropy production due to internal processes was not included, and the 2nd law was thus practically removed from the Gibbs combined law, so it is only applicable to systems under equilibrium. Gibbs further derived the classical statistical thermodynamics in terms of the probability of configurations in a system. With the quantum mechanics (QM) developed, the QM-based statistical thermodynamics was established and connected to classical statistical thermodynamics at the classical limit as shown by Landau. The development of density function theory (DFT) by Kohn and co-workers enabled the QM prediction of properties of the ground state of a system. On the other hand, the entropy production due to internal processes in non-equilibrium systems was studied separately by Onsager and Prigogine and co-workers. The digitization of thermodynamics was developed by Kaufman in the framework of the CALPHAD modeling of individual phases. Our recently termed zentropy theory integrates DFT and statistical mechanics through the replacement of the internal energy of each individual configuration by its DFT-predicted free energy. Furthermore, through the combined law of thermodynamics with the entropy production as a function of internal degrees of freedom, it is shown that the kinetic coefficient matrix of independent internal processes is diagonal with respect to the conjugate potentials in the combined law, and the cross phenomena represented by the phenomenological Onsager reciprocal relationships are due to the dependence of the conjugate potential of the molar quantity in a flux on nonconjugate potentials.