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Relative thermalization.

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Quantum entanglement allows heat to flow from cold to hot systems, challenging thermodynamics. A stronger definition of thermalization, requiring local thermal states and no correlation with a quantum reference, restores thermodynamic laws for nanoscale systems.

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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.