The steepest-entropy-ascent quantum thermodynamic (SEAQT) framework is used to model the decoherence that occurs during the state evolution of two different microscopic composite systems. The test cases are a composite system and a particle-photon field composite system like that experimentally studied in cavity quantum electrodynamics. The first system is used to study the characteristics of the nonlinear equation of motion of the SEAQT framework when modeling the state evolution of a microscopic composite system with particular interest in the phenomenon of decoherence. The second system is used to compare the numerical predictions of the SEAQT framework with experimental cavity quantum electrodynamic data available in the literature. For the two different numerical cases presented, the time evolution of the density operator of the composite system as well as that of the reduced operators belonging to the two constituents is traced from an initial nonequilibrium state of the composite along its relaxation towards stable equilibrium. Results show for both cases how the initial entanglement and coherence is dissipated during the state relaxation towards a state of stable equilibrium.