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Gradient Echo Quantum Memory in Warm Atomic Vapor
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Derivation of quantum work equalities using a quantum Feynman-Kac formula.

Fei Liu1

  • 1School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China. feiliu@buaa.edu.cn

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary

This study introduces a new method for deriving nonequilibrium work equalities in isolated quantum systems, building upon the Feynman-Kac formula. The approach yields results similar to classical fluctuation relations.

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Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Non-equilibrium thermodynamics

Background:

  • The Feynman-Kac formula is a cornerstone in bridging quantum mechanics and stochastic processes.
  • Nonequilibrium work equalities, such as the Jarzynski and Bochkov-Kuzovlev equalities, are crucial for understanding energy fluctuations in driven systems.
  • Existing methods for deriving these equalities in quantum systems can be complex and differ significantly from classical approaches.

Purpose of the Study:

  • To develop a novel method for deriving nonequilibrium work equalities in isolated quantum systems.
  • To establish a formal connection between quantum and classical approaches to fluctuation relations.
  • To provide a more unified framework for studying thermodynamics in driven quantum systems.

Main Methods:

  • Utilized a quantum mechanical analog of the Feynman-Kac formula.
  • Applied this analog to derive general nonequilibrium work equalities for isolated quantum systems.
  • Compared the derived quantum equalities with their classical counterparts and existing quantum methods.

Main Results:

  • Successfully derived key nonequilibrium work equalities, including the Jarzynski and Bochkov-Kuzovlev equalities, from the quantum Feynman-Kac analog.
  • The developed method yields quantum work relations that are formally similar to those derived for classical systems.
  • Demonstrated a closer structural resemblance to classical fluctuation relation derivations than previous quantum methods.

Conclusions:

  • The quantum mechanical analog of the Feynman-Kac formula provides an effective pathway to derive nonequilibrium work equalities.
  • This method unifies the treatment of fluctuation relations across quantum and classical regimes.
  • The findings offer a more intuitive and potentially simpler approach to quantum thermodynamics research.