Steepest-entropy-ascent quantum thermodynamics (SEAQT) is an intriguing approach that describes equilibrium and dynamic processes in a self-consistent way. To date, it has been applied primarily to gas phase systems because of the difficulty in generating the complex eigenstructures (eigenvalues and eigenfunctions) associated with solid or liquid phases. In this contribution, the SEAQT modeling is extended to the solid phase by constructing a so-called pseudo-eigenstructure, and its applicability is demonstrated by calculating the thermal expansion of metallic silver for three cases: (a) stable equilibrium, (b) along three irreversible paths from different initial non-equilibrium states to stable equilibrium, and (c) along an irreversible path between two stable equilibrium states. The SEAQT framework with an anharmonic pseudo-eigenstructure predicts reasonable values for the equilibrium thermal expansion. For the irreversible cases considered, the SEAQT approach makes it possible to predict the time-dependence of lattice relaxations from the initial state to the final equilibrium state.