A Description of the Quantum Mpemba Effect using the Steepest-Entropy-Ascent Quantum Thermodynamics Framework

The quantum Mpemba effect is a phenomenon characterized by an exponential relaxation from a non-equililbrium state to a steady state. This effect was predicted with an analysis of the Liouvillian superoperator and experimentally demonstrated in a three-level system. In this work, the system dynamics of the Mpemba effect is predicted within the steepest-entropy-ascent quantum thermodynamics framework considering a single constituent three-level isolated system. The system is projected from a four-dimensional Hilbert space onto a three-dimensional one using the Feshbach projection in order to compare the theoretical results with experimental data. Since the quantum Mpemba effect is characterized by a dissipative acceleration, the relaxation parameter, $\tau_D$, plays a fundamental rol in the dissipative dynamics predicted by the model and is determined using machine learning methods, resulting in a model that thermodynamically describes this phenomenon at the quantum level.