Zentropy—A Theory for Prediction of Observables

An emergent property appears when a number of simple entities interact in an environment to form more complex behaviors collectively that any single entity does not exhibit. Emergent properties are hard to predict because the number of interactions between a system's components increases exponentially with the number of components. In principle, the elegant Schrödinger equation in quantum mechanics could address the multibody interactions, resulting in the standard statistical mechanics where the individual entities are pure quantum states with zero entropy and their partition functions related to their internal energies. The applications of the Schrödinger equation to complex systems are made possible by the density functional theory (DFT) that postulates the existence of a unique electron density for the ground state of a system at 0 K. Using the ground and non-ground states as the building entities of complex systems, we propose that the entropy of a complex system is composed of the weighted sum of entropies of its building entities plus the classical statistical entropy among the entities. This new theory, termed as Zentropy theory, stacks up the entropic contributions from electrons to the scale of complex system of interest and result in the partition functions of building entities related to their free energies instead of their internal energies. With the properties of ground and non-ground states obtained from DFT, we show that the emergent properties in some magnetic and ferroelectric systems, previously thought to be explainable exclusively by strongly correlated physics, can be predicted, including singularity at critical points. This further provides a theoretical framework to predict emergent cross phenomena, including thermoelectricity, thermodiffusion, electrocaloric effect, and thermal expansion of material systems (https://doi.org/10.1080/21663831.2022.2054668).