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

Abstract

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, $τ_D$, 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.

Figures (16)

• Figure 1: Experimental implementation of the Mpemba effect Zhang et al.zhang2025observation.
• Figure 2: Population dynamics of the SEAQT model with $\tau_D = \tau_D(t)$ for the three initial conditions: a) $|0\rangle\langle0|$, b)$|2\rangle\langle2|$, and c)$|\mathrm{sME}\rangle\langle\mathrm{sME}|$.
• Figure 3: Population dynamics of the Lindblad model for the three initial conditions: a) $|0\rangle\langle0|$, b)$|2\rangle\langle2|$, and c)$|\mathrm{sME}\rangle\langle\mathrm{sME}|$.
• Figure 4: Time evolution of the relaxation parameter, $\tau_D = \tau_D(t)$ for the SEAQT model.
• Figure 5: Energy and entropy evolution for the SEAQT model with $\tau_D = \tau_D(t)$: a) state evolution represented on the energy-entropy diagram, b) energy expectation value, and c) entropy expectation value.