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Fluctuation theorems for quantum master equations.

Massimiliano Esposito1, Shaul Mukamel

  • 1Department of Chemistry, University of California, Irvine, California 92697, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 23, 2006
PubMed
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This study derives a quantum fluctuation theorem for driven quantum subsystems using a quantum master equation. It naturally introduces quantum trajectories and thermodynamic quantities, extending classical fluctuation theorems to the quantum realm.

Area of Science:

  • Quantum thermodynamics
  • Statistical mechanics
  • Quantum information theory

Background:

  • Understanding thermodynamic laws in quantum systems is crucial.
  • Quantum master equations (QME) describe open quantum systems.
  • Fluctuation theorems connect microscopic dynamics to macroscopic thermodynamics.

Purpose of the Study:

  • Derive a quantum fluctuation theorem for driven quantum subsystems.
  • Establish a connection between quantum master equations and fluctuation theorems.
  • Extend classical fluctuation theorems to quantum dynamics.

Main Methods:

  • Derivation based on the assumption of a closed evolution equation for the reduced density matrix (quantum master equation).
  • Transformation to a time-dependent Liouville space basis that diagonalizes the instantaneous reduced density matrix.

Related Experiment Videos

  • Utilizing quantum trajectories to naturally define entropy, heat, and work.

    • Main Results:

    • A quantum fluctuation theorem for driven quantum subsystems is derived.
    • Quantum trajectories and associated thermodynamic quantities (entropy, heat, work) emerge naturally from the QME.
    • Quantum integral fluctuation theorem, steady-state fluctuation theorem, and Jarzynski relation are established.

    Conclusions:

    • The quantum master equation provides a foundation for quantum fluctuation theorems.
    • The framework naturally unifies quantum dynamics with thermodynamic concepts.
    • This work bridges classical and quantum statistical mechanics through fluctuation theorems.