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Quantum work fluctuations in connection with the Jarzynski equality.

Juan D Jaramillo1, Jiawen Deng2, Jiangbin Gong1,2

  • 1Department of Physics, National University of Singapore, Singapore 117546.

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|January 20, 2018
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Summary
This summary is machine-generated.

The Jarzynski equality relates free energy to work. Nonadiabatic protocols cause work fluctuations to diverge, especially in quantum systems, complicating experimental verification.

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Area of Science:

  • Statistical mechanics
  • Quantum thermodynamics
  • Non-equilibrium systems

Background:

  • The Jarzynski equality is a key result in non-equilibrium statistical mechanics, linking equilibrium free energy differences to ensemble averages of work done during non-equilibrium processes.
  • Experimental verification of the Jarzynski equality relies on the statistical properties of work measurements, specifically the variance of the exponential work term.

Purpose of the Study:

  • To investigate the behavior of work fluctuations (variance of e^{-βW}) in Hamiltonian systems under nonadiabatic protocols.
  • To identify conditions under which these fluctuations diverge and their implications for testing the Jarzynski equality.

Main Methods:

  • Theoretical analysis of work fluctuations in harmonic and anharmonic Hamiltonian systems.
  • Examination of a quantum harmonic oscillator with a time-dependent trapping frequency as a model system.

Main Results:

  • Work fluctuations (variance of e^{-βW}) systematically diverge in nonadiabatic protocols for both harmonic and anharmonic systems.
  • This divergence is observed even when adiabatic protocols do not exhibit such behavior, suggesting a dynamically induced phase transition in work fluctuations.
  • For a quantum harmonic oscillator, nonadiabatic protocols lead to diverging work fluctuations at low temperatures, contrasting with classical systems.

Conclusions:

  • Diverging work fluctuations indicate that nonadiabatic protocols drive systems too far from equilibrium for reliable Jarzynski equality testing.
  • Designed control fields are necessary to suppress quantum work fluctuations and enable accurate experimental verification of the Jarzynski equality.