The equation of motion of steepest-entropy-ascent quantum thermodynamics (SEA-QT) was first postulated in the early 1980s with the intent of modeling the non-linear dynamic behavior encountered in nature, which the unitary (linear) dynamics of the Schrödinger-von Neumann equation cannot. The SEA-QT equation is used here to model the decoherence phenomenon between two distinguishable and indivisible elementary constituents of type spin–½ (e.g., quantum bits or qubits). The resulting set of non-linear, first-order differential equations is solved with a fourth-order-Runge-Kutta routine provided by Matlab®. The time evolution of the state of the composite system as well as that of the reduced and locally-perceived states of the two constituents are traced from an initial non-equilibrium state of the composite along its relaxation towards stable equilibrium at constant system energy. An entangled and generally coherent, initial non-equilibrium state of the composite quantum system is prepared using a heuristic approach, which consists of randomly and homogeneously generating an initial point on the Bloch sphere for each of the constituents and then using a weighted average of their projections to arrive at an initial state for the composite. Results show how the initial entanglement and coherence between the two spin–½ constituents are reduced during relaxation towards a state of stable equilibrium. When the two particles are non-interacting, the initial coherence is lost once stable equilibrium is reached. When they are interacting, the coherence in the final stable equilibrium state is only that due to the interaction.

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