  Today's thermodynamics is largely based on the combined law for equilibrium
systems and statistical mechanics derived by Gibbs in 1873 and 1901,
respectively, while irreversible thermodynamics for nonequilibrium systems
resides essentially on the Onsager Theorem as a separate branch of
thermodynamics developed in 1930s. Between them, quantum mechanics was invented
and was quantitatively solved in terms of density functional theory (DFT) in
1960s. These three scientific domains operate based on different principles and
are very much separated from each other. In analogy to the parable of the blind
men and the elephant articulated by Perdew, they individually represent
different portions of a complex system and thus are incomplete by themselves
alone, resulting in the lack of quantitative agreement between their
predictions and experimental observations. Over the last two decades, the
author's group has developed a multiscale entropy approach (recently termed as
zentropy theory) that integrates DFT-based quantum mechanics and Gibbs
statistical mechanics and is capable of accurately predicting entropy and free
energy of complex systems. Furthermore, in combination with the combined law
for nonequilibrium systems developed by Hillert, the author developed the
theory of cross phenomena beyond the phenomenological Onsager Theorem. The
zentropy theory and theory of cross phenomena jointly provide quantitative
predictive theories for systems from electronic to any observable scales as
reviewed in the present work.
