Thermodynamics of the Quantum Mpemba Effect

Area of Science:

• Quantum thermodynamics
• Nonequilibrium quantum systems
• Quantum statistical mechanics

Background:

• The Mpemba effect describes the counterintuitive phenomenon where hotter water can freeze faster than colder water.
• Understanding this effect in quantum systems requires a framework of nonequilibrium quantum thermodynamics.
• Previous studies have explored classical and quantum aspects, but a unified thermodynamic perspective is needed.

Purpose of the Study:

• To investigate the quantum Mpemba effect from the viewpoint of nonequilibrium quantum thermodynamics.
• To identify the conditions under which a quantum system exhibits an accelerated relaxation to equilibrium.
• To establish a theoretical basis for the quantum Mpemba effect using thermodynamic principles.

Main Methods:

• Studying the relaxation dynamics of quantum systems coupled to a Markovian heat bath, modeled by Davies maps.
• Analyzing systems starting from a state with energy eigenbasis coherences.
• Utilizing unitary transformations to modify initial states and observe their effect on relaxation times.
• Calculating nonequilibrium free energy and irreversible entropy production.

Main Results:

• An exponential speedup to equilibrium is demonstrated when a quantum state with coherences is transformed into a diagonal state in the energy eigenbasis, provided the generator's spectral gap is defined by a complex eigenvalue.
• This accelerated relaxation is identified as a genuine quantum Mpemba effect when the transformed state possesses higher nonequilibrium free energy.
• The study shows that a unitary transformation can always be constructed to induce this effect.
• Demonstrated findings through analysis of nonequilibrium free energy and irreversible entropy production in single and multiqubit systems.

Conclusions:

• The quantum Mpemba effect can be understood within the framework of nonequilibrium quantum thermodynamics.
• Specific initial state preparation and transformations are key to observing accelerated quantum relaxation.
• The findings provide a theoretical foundation for the quantum Mpemba effect and its potential experimental realization.