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The Replica Exchange Wang-Landau Method is used to estimate the energy landscape of a polymer composed of a simple hydrophobic and polar sequence using the HP protein model. Calculations of state transitions between the energy levels of the derived energy landscape are made using an equation of motion from the steepest-entropy-ascent quantum thermodynamic (SEAQT) framework. The SEAQT framework makes it possible to determine the unique kinetic paths from an arbitrary quasi-equilibrium or non-equilibrium initial state to stable equilibrium. Calculations performed with SEAQT require significantly reduced computational time versus comparable Monte Carlo simulations while providing otherwise unavailable thermodynamic and structural properties. Expected values for state averaged structural parameters are used to produce representative reconstructions of the calculated state-based evolution. Results show continuous transitions between states with no distinct folding phases. Changes in chain conformations during heating and cooling are more drastic along non-equilibrium paths than along quasi-equilibrium paths. In addition, SEAQT-derived kinetics are compared to experimentally derived intensity profiles describing the kinetics of the cytochrome c protein using Rouse dynamic relations.