This paper investigates the quantum Mpemba effect from the perspective of non-equilibrium quantum thermodynamics using Davies maps. The Mpemba effect is a phenomenon where a hotter system reaches equilibrium faster than a cooler one. The authors demonstrate that by transforming a quantum state to be diagonal in the energy eigenbasis, an exponential speedup to equilibrium can occur if the generator's spectral gap is defined by a complex eigenvalue. This transformation increases the non-equilibrium free energy and leads to a genuine quantum Mpemba effect. The study shows that a unitary transformation can always be constructed to achieve this effect, and the findings are illustrated using single and multi-qubit examples. The paper also discusses the thermodynamic significance of the non-equilibrium free energy and the irreversible entropy production in quantum systems. The results highlight the importance of the generator's structure in thermalising open quantum systems and provide a framework for understanding the quantum Mpemba effect in various physical systems. The study contributes to the broader understanding of quantum thermodynamics and has potential applications in dissipative state engineering.This paper investigates the quantum Mpemba effect from the perspective of non-equilibrium quantum thermodynamics using Davies maps. The Mpemba effect is a phenomenon where a hotter system reaches equilibrium faster than a cooler one. The authors demonstrate that by transforming a quantum state to be diagonal in the energy eigenbasis, an exponential speedup to equilibrium can occur if the generator's spectral gap is defined by a complex eigenvalue. This transformation increases the non-equilibrium free energy and leads to a genuine quantum Mpemba effect. The study shows that a unitary transformation can always be constructed to achieve this effect, and the findings are illustrated using single and multi-qubit examples. The paper also discusses the thermodynamic significance of the non-equilibrium free energy and the irreversible entropy production in quantum systems. The results highlight the importance of the generator's structure in thermalising open quantum systems and provide a framework for understanding the quantum Mpemba effect in various physical systems. The study contributes to the broader understanding of quantum thermodynamics and has potential applications in dissipative state engineering.