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Quantum Jarzynski equality of measurement-based work extraction.

Yohei Morikuni1, Hiroyasu Tajima2, Naomichi Hatano3

  • 1Department of Physics, The University of Tokyo, Komaba, Meguro, Tokyo 153-8505, Japan.

Physical Review. E
|April 19, 2017
PubMed
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This study questions common assumptions in quantum heat engines. It shows that unitary dynamics are inappropriate and derives a quantum Jarzynski equality, revealing fluctuations in work extraction for non-cyclic processes.

Area of Science:

  • Quantum Thermodynamics
  • Statistical Mechanics
  • Quantum Information

Background:

  • Quantum heat engines often assume unitary system dynamics and equate extracted work with internal energy loss.
  • These assumptions are critical for understanding energy conversion at the quantum scale.

Purpose of the Study:

  • To scrutinize the assumptions of unitary dynamics and work-energy equivalence in quantum heat engines.
  • To analyze quantum heat engines using a measurement-based formulation of work extraction.
  • To derive and investigate the quantum Jarzynski equality for quantum heat engines.

Main Methods:

  • Analysis of a two-level quantum system to demonstrate the limitations of unitary time evolution.
  • Application of the measurement-based work extraction formulation by Hayashi and Tajima.

Related Experiment Videos

  • Derivation of the quantum Jarzynski equality within this framework.

    • Main Results:

    • The variance of transferred energy diverges when approximating internal system dynamics as unitary.
    • The derived quantum Jarzynski equality shows fluctuations for non-cyclic processes, often exceeding unity.
    • The right-hand side of the equality simplifies to unity for natural cyclic processes.

    Conclusions:

    • Unitary time evolution is an inappropriate assumption for internal system dynamics in quantum heat engines.
    • The derived quantum Jarzynski equality provides a testable prediction for experimental verification.
    • The measurement-based formulation offers a more accurate description of work extraction in quantum systems.