  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.
