The proposed research developed the zentropy theory through applications to complex magnetic materials and superconductors under the hypothesis that the emergent properties of complex magnetic materials and superconductors can be predicted by statistical mechanics of ergodic microstates with their partition functions computed from DFT-predicted free energies. The key objective is to develop approaches to systematically determine the types and number of microstates and the supercell size in DFT-based calculations through convergency of macroscopic functionalities, with the incorporation of our mixed-space approach accounting for the interactions between periodic supercells. In addition to use scientific intuitions to guide the design of important microstates, the key innovation of the proposed research is to integrate the domain knowledge and the material-property-descriptor database (MPDD) with 4 million microstates, which is supported by our deep neural network machine learning models (SIPFENN: structure-informed prediction of formation energy using neural networks) and integrated with our high throughput DFT Tool Kit (DFTTK). For complex magnetic materials, one of the objectives is to develop approaches to calculate short-range ordering from the statistical distribution of each microstate. For superconductors, the divergency of quasiparticle effective mass at a quantum critical point will be investigated, and the superconducting and non-superconducting microstates will be d

Thermodynamics of a photon gas and deformed dispersion relations We resort to the methods of statistical mechanics in order to determine the effects that a deformed dispersion relation has upon the thermodynamics of a photon gas. The ensuing modifications to the density of states, partition function, pressure, internal energy, entropy, and specific heat are calculated. It will be shown that the breakdown of Lorentz invariance can be interpreted as a repulsive interaction, among the photons. Additionally, it will be proved that the presence of a deformed dispersion relation entails an increase in the entropy of the system. In other words, as a consequence of the loss of the aforementioned symmetry the number of microstates available to the corresponding equilibrium state grows. Published as: Gen.Rel.Grav.39:1175-1183,2007 DOI: 10.1007/s10714-007-0419-1 arXiv categories: gr-qc

“Disorder” was the consequence, to Boltzmann, of an initial “order” not — as is obvious today — of what can only be called a “prior, lesser but still humanly-unimaginable, large number of accessible microstate - Microstates - Dictionaries define “macro” as large and “micro” as very small but a macrostate and a microstate in thermodynamics aren't just definitions of big and little sizes of chemical systems. Instead, they are two very different ways of looking at a system. A microstate is one of the huge number of different accessible arrangements of the molecules' motional energy* for a particular macrostate. - Simple Entropy Changes - Examples - Several Examples are given to demonstrate how the statistical definition of entropy and the 2nd law can be applied. Phase Change, gas expansions, dilution, colligative properties and osmosis. - Statistical Entropy - Entropy is a state function that is often erroneously referred to as the 'state of disorder' of a system.

On the relationship between molecular spectroscopy and statistical mechanics: Calculation of partition functions for triatomic molecules undergoing large-amplitude bending vibrations