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Sum rule for fluctuations of work.

Hyogeon Park1, Yong Woon Kim1, Juyeon Yi2

  • 1Department of Physics, <a href="https://ror.org/05apxxy63">Korea Advanced Institute of Science and Technology</a>, Deajeon 34141, Korea.

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We derived a new sum rule for work fluctuations in quantum systems, simplifying to a linear relation between work average and its second moment. This finding is numerically confirmed for a spin model, advancing quantum thermodynamics understanding.

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Area of Science:

  • Quantum Thermodynamics
  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Understanding work fluctuations is crucial in non-equilibrium quantum processes.
  • Existing equalities like Jarzynski equality provide insights but may not cover all quantum stationary ensembles.

Purpose of the Study:

  • To derive a general sum rule for work moments in quantum stationary ensembles.
  • To explore the implications of this sum rule for canonical ensembles and simplified relationships.

Main Methods:

  • Theoretical derivation of a sum rule for work moments.
  • Application to quantum stationary ensembles, including the canonical ensemble.
  • Numerical verification using exact diagonalization of a spin model.

Main Results:

  • An exact sum rule satisfied by work moments was obtained for a broad class of quantum stationary ensembles.
  • The sum rule reproduces the Jarzynski equality for the canonical ensemble.
  • A simplified linear relationship between the work average and the second moment of work was identified.

Conclusions:

  • The derived sum rule offers a new perspective on work fluctuations in quantum systems.
  • The simplified linear relationship provides a testable prediction and was numerically validated.
  • This work bridges theoretical insights with numerical evidence in quantum statistical mechanics.