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

TL;DR

This paper models the quantum Mpemba effect using the steepest-entropy-ascent quantum thermodynamics framework, predicting system dynamics and fitting experimental data with machine learning-enhanced parameters.

Contribution

It introduces a quantum thermodynamic model for the Mpemba effect, incorporating a relaxation parameter optimized via machine learning, and compares theoretical predictions with experimental results.

Findings

The model predicts exponential relaxation consistent with experimental data.

The relaxation parameter $ au_D$ is effectively determined using machine learning.

The framework provides a thermodynamic description of the quantum Mpemba effect.

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, $\tau_D$, 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.