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Steepest Entropy Ascent Quantum Thermodynamics (SEAQT) is a novel theoretical framework unifying quantum mechanics and thermodynamics. This framework employs an equation of motion governed by the principle of steepest entropy ascent to determine the thermodynamic state evolution of modeled systems. The SEAQT framework has seen applied to multiple systems, including quantum and gas phase systems, in addition to solid-state material phenomena. A precise definition of entropy is crucial for the application of this framework. The SEAQT framework defines entropy in terms of an intrinsic property associated with the energy spectrum of a modeled system, namely degeneracy. The degeneracy, or density of states, is the number of unique system configurations for a given energy level. Calculating this quantity is often difficult, limiting many solid-state material studies to the few systems with analytical expressions which define the degeneracy. However, the use of the Replica Exchange Wang Landau (REWL) algorithm has alleviated these challenges. The REWL algorithm is a non-Markovian MC method capable of estimating the density of the state of any discretely described system. Employing the derived discrete energy spectrum and associated degeneracies, combined with the SEAQT equation of motion, has allowed for the investigation of previously indescribable systems. Detail of the complete methods are provided in this document, and the prediction of system kinetics are presented for capillary dynamics, protein folding, polymer brush conformal evolution, and ion sequestration using polymers. The results from each model are compared against experimental results for the thermodynamic paths of systems under varying system conditions are shown. Use of the combined framework has predicted (i) expected grain growth for ceramic and nanoscale metallic systems, (ii) expected conformal evolution of initial collapse of a simple polymer chain, (ii) equilibrium density profile evolution of a polymer brush, (iv) expected functional participation in sequestration of ions in a polar solvent. / Doctor of Philosophy / In this document, a novel computational method is presented for the modeling of various metallic, ceramic and polymeric materials. The computational framework and methodology presented does not model the mechanical evolution of material systems, instead it focuses on a holistic approach accounting for all possible formations, configurations, and associated energies. The basics of the presented frame have seen significant application to several systems of various length scales, though material applications were limited due to the necessity of applying derived analytical expressions from literature. This work expands the application of the method to arbitrary systems, removing prior limitations to simulate several previously indescribable systems. Significant benefits of the presented methods include rapid calculation of the system evolution under variable initial thermal conditions versus conventional models.

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