  The steepest-entropy-ascent quantum thermodynamic (SEAQT) framework was used
to calculate the stability of a collection of point defects in 2D PtSe$_2$ and
predict the kinetics with which defects rearrange during thermal annealing. The
framework provides a non-equilibrium, ensemble-based framework with a
self-consistent link between mechanics (both quantum and classical) and
thermodynamics. It employs an equation of motion derived from the principle of
steepest entropy ascent (maximum entropy production) to predict the time
evolution of a set of occupation probabilities that define the states of a
system undergoing a non-equilibrium process. The system is described by a
degenerate energy landscape of eigenvalues, and the entropy is found from the
occupation probabilities and the eigenlevel degeneracies. Scanning tunneling
microscopy was used to identify the structure and distribution of point defects
observed experimentally in a 2D PtSe$_2$ film. A catalog of observed defects
included six unique point defects (vacancies and anti-site defects on Pt and Se
sublattices) and twenty combinations of multiple point defects in close
proximity. The defect energies were estimated with density functional theory
(DFT), while the degeneracies, or density of states, for the 2D film with all
possible combinations or arrangements of cataloged defects was constructed
using a non-Markovian Monte-Carlo approach (i.e., the
Replica-Exchange-Wang-Landau algorithm) with a q-state Potts model. The energy
landscape and associated degeneracies were determined for a 2D PtSe$_2$ film
two molecules thick and $30 \times 30$ unit cells in area (total of 5400
atoms). The SEAQT equation of motion was applied to the energy landscape to
determine how an arbitrary density and arrangement of the six defect types
evolve during annealing.
