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Quantum fluctuation theorems and generalized measurements during the force protocol.

Gentaro Watanabe1, B Prasanna Venkatesh2, Peter Talkner3

  • 1Asia Pacific Center for Theoretical Physics (APCTP), San 31, Hyoja-dong, Nam-gu, Pohang, Gyeongbuk 790-784, Korea and Department of Physics, POSTECH, San 31, Hyoja-dong, Nam-gu, Pohang, Gyeongbuk 790-784, Korea.

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Generalized measurements in quantum systems can satisfy fluctuation relations like the Jarzynski equality and Crooks relation under specific conditions. These conditions ensure the validity of these important thermodynamic relations for quantum measurements.

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Area of Science:

  • Quantum Thermodynamics
  • Statistical Mechanics
  • Quantum Measurement Theory

Background:

  • Generalized measurements on quantum systems are crucial for understanding quantum thermodynamics.
  • The Jarzynski equality and Crooks relation are fundamental in non-equilibrium statistical mechanics.
  • Previous work established these relations for projective measurements in quantum systems.

Purpose of the Study:

  • To investigate generalized measurements of observables during quantum force protocols.
  • To formulate conditions for the validity of the Jarzynski equality and Crooks relation under generalized measurements.
  • To explore the implications of selective measurements and information gain on these fluctuation relations.

Main Methods:

  • Analysis of generalized measurement operators during forward and backward quantum protocols.
  • Formulation of normalization conditions for measurement operators.
  • Investigation of selective measurements using joint probability density functions.

Main Results:

  • Jarzynski equality holds for projective measurements and requires specific normalization for generalized measurements.
  • Crooks relation necessitates interdependency between forward and backward measurement operators.
  • Selective measurements lead to a modified Crooks relation involving information gain.

Conclusions:

  • Generalized measurements require specific conditions to satisfy fluctuation relations.
  • The relationship between forward and backward measurement operators is key for Crooks relation validity.
  • Information gain quantifies modifications to the Crooks relation in selective quantum measurements.