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Work extraction from a single energy eigenstate.

Kazuya Kaneko1, Eiki Iyoda1, Takahiro Sagawa1

  • 1Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.

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Summary

Extracting work from individual quantum energy eigenstates is impossible, even from a single state. This finding suggests quantum chaos enforces a stronger second law of thermodynamics than previously understood.

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Area of Science:

  • Quantum thermodynamics
  • Statistical mechanics
  • Quantum chaos

Background:

  • The second law of thermodynamics prohibits work extraction from equilibrium states (Gibbs ensemble).
  • The eigenstate thermalization hypothesis (ETH) posits that single energy eigenstates represent thermal equilibrium.

Purpose of the Study:

  • To reconcile the second law with ETH by investigating work extraction from individual energy eigenstates.
  • To determine if work can be extracted from a single quantum state.

Main Methods:

  • Numerical exact diagonalization of a quantum quench protocol.
  • Analysis of local Hamiltonians and their nonintegrable properties.
  • Evaluation of work-extractable energy eigenstates in finite systems.

Main Results:

  • Work extraction from any single energy eigenstate was found to be exactly zero in finite systems.
  • This impossibility holds when prequench or postquench Hamiltonians are nonintegrable.
  • The ETH for nonlocal observables explains this phenomenon.

Conclusions:

  • Quantum chaos, indicated by nonintegrability, strengthens the second law of thermodynamics.
  • The study implies a more rigorous application of thermodynamic laws at the quantum level.