Relative thermalization

Area of Science:

• Quantum thermodynamics
• Statistical mechanics
• Quantum information theory

Background:

• Quantum systems can exhibit non-classical thermodynamic behavior due to entanglement.
• Traditional thermodynamics may not fully apply to highly entangled quantum systems.
• Nanoscale quantum systems require advanced thermodynamic frameworks.

Purpose of the Study:

• To reconcile quantum mechanics with thermodynamic laws.
• To introduce a robust definition of thermalization for quantum systems.
• To establish conditions for thermodynamic consistency in quantum thermodynamics.

Main Methods:

• Derivation of a technical condition for relative thermalization.
• Utilizing conditional entropies to define thermalization.
• Analysis of quantum systems with general quantum references.

Main Results:

• A stronger notion of thermalization is proposed: a system is thermal relative to a reference if it is locally thermal and uncorrelated.
• This stronger definition recovers traditional thermodynamic laws, even with quantum entanglement.
• Established results on local thermalization are shown to be special cases.

Conclusions:

• Relative thermalization provides a framework to apply thermodynamics to quantum systems.
• The findings are crucial for understanding thermodynamics in nanoscale quantum devices.
• The derived condition based on conditional entropies offers a practical tool for analysis.