Zentropy theory for accurate prediction of free energy, volume, and thermal expansion without fitting parameters

TL;DR

This paper introduces zentropy theory, combining quantum and statistical mechanics, to accurately predict free energy, volume, and thermal expansion, including negative thermal expansion, without fitting parameters.

Contribution

The paper presents a novel zentropy theory that predicts thermodynamic properties directly from quantum mechanics and statistical probabilities without empirical fitting.

Findings

Predicts negative thermal expansion due to symmetry-breaking configurations.

Accurately calculates volume and free energy without fitting parameters.

Integrates quantum mechanics with statistical mechanics for property prediction.

Abstract

Based on statistical mechanics, a macroscopically homogeneous system, i.e., a single phase in the present context, is composed of many independent configurations that the system embraces. The macroscopical properties of the system are determined by the properties and statistical probabilities of those configurations with respect to external conditions. The volume of a single phase is thus the weighted sum of the volumes of all configurations. Consequently, the derivative of the volume to temperature of a single phase depends on both the derivatives of the volumes of every configuration to temperature and the derivatives of their statistical probabilities to temperature with the latter introducing non-linear emergent behaviors. It is shown that the derivative of the volume to temperature of the single phase can be negative, i.e., negative thermal expansion (NTE), due to the symmetry-breaking non-ground-state configurations with smaller volumes than that of the ground-state configuration and the rapid increase of the statistical probabilities of the former, and NTE can be predicted without fitting parameters from the zentropy theory that combines quantum mechanics and statistical mechanics with the free energy of each configuration predicted from quantum mechanics and the partition function of each configuration calculated from its free energy.