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Clock-Work Trade-Off Relation for Coherence in Quantum Thermodynamics.

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Area of Science:

  • Quantum Thermodynamics
  • Quantum Information Theory
  • Statistical Mechanics

Background:

  • Quantum coherences, superpositions of energy eigenstates, exhibit nonclassical thermodynamic behavior.
  • Understanding the energetic and functional roles of quantum coherence is crucial for quantum thermodynamics.

Purpose of the Study:

  • To differentiate and characterize two distinct forms of thermodynamic coherence: internal and external.
  • To investigate the energetic value of internal coherence and the metrological potential of external coherence.
  • To establish a fundamental trade-off relation between these two types of coherence.

Main Methods:

  • Theoretical analysis of quantum states and their thermodynamic properties.
  • Derivation of dynamical constraints for external coherence related to quantum metrology.
  • Formulation of a clock-work trade-off relation under minimal thermodynamic assumptions.

Main Results:

  • Thermodynamic coherence is classified into internal (energetic work value) and external (quantum clock function) types.
  • Demonstration of quantum states with finite internal coherence but zero deterministic work value.
  • Establishment of a universal clock-work trade-off relation bounding the combined resources.

Conclusions:

  • The study introduces a novel framework for understanding quantum coherence in thermodynamics.
  • The derived clock-work trade-off offers a quantum thermodynamic analogue to time-energy conjugacy.
  • This work provides fundamental insights into the interplay between work extraction and timekeeping in quantum systems.