Application of Steepest-Entropy-Ascent Quantum Thermodynamics to Solid-State Phenomena

Steepest-entropy-ascent quantum thermodynamics (SEAQT) is a mathematical and theoretical framework for intrinsic quantum thermodynamics (IQT), a unified theory of quantum mechanics and thermodynamics. In the theoretical framework, entropy is viewed as a measure of energy load sharing among available energy eigenlevels, and a unique relaxation path of a system from an initial non-equilibrium state to a stable equilibrium is determined from the greatest entropy generation viewpoint. The SEAQT modeling has seen a great development recently. However, the applications have mainly focused on gas phases, where a simple energy eigenstructure (a set of energy eigenlevels) can be constructed from appropriate quantum models by assuming that gas-particles behave independently. The focus of this research is to extend the applicability to solid phases, where interactions between constituent particles play a definitive role in their properties so that an energy eigenstructure becomes quite complicated and intractable from quantum models. To cope with the problem, a highly simplified energy eigenstructure (so-called ``pseudo-eigenstructure") of a condensed matter is constructed using a reduced-order method, where quantum models are replaced by typical solid-state models. The details of the approach are given and the method is applied to make kinetic predictions in various solid-state phenomena: the thermal expansion of silver, the magnetization of iron, and the continuous/discontinuous phase separation and ordering in binary alloys where a pseudo-eigenstructure is constructed using atomic/spin coupled oscillators or a mean-field approximation. In each application, the reliability of the approach is confirmed and the time-evolution processes are tracked from different initial states under varying conditions (including interactions with a heat reservoir and external magnetic field) using the SEAQT equation of motion derived for each specific application. Specifically, the SEAQT framework with a pseudo-eigenstructure successfully predicts: (i) lattice relaxations in any temperature range while accounting explicitly for anharmonic effects, (ii) low-temperature spin relaxations with fundamental descriptions of non-equilibrium temperature and magnetic field strength, and (iii) continuous and discontinuous mechanisms as well as concurrent ordering and phase separation mechanisms during the decomposition of solid-solutions.