Moments of work in the two-point measurement protocol for a driven open quantum system

Abstract

We study the distribution of work induced by the two-point measurement protocol for a driven open quantum system. We first derive a general form for the generating function of work for the total system, bearing in mind that the Hamiltonian does not necessarily commute with its time derivative. Using this result we then study the first few moments of work by using the master equation of the reduced system, invoking approximations similar to the ones made in the microscopic derivation of the reduced density matrix. Our results show that, already in the third moment of work, correction terms appear that involve commutators between the Hamiltonian and its time derivative. To demonstrate the importance of these terms, we consider a sinusoidally, weakly driven and weakly coupled open two-level quantum system, and indeed find that already in the third moment of work the correction terms are significant. We also compare our results to those obtained with the quantum jump method and find a good agreement.

9 pages, 3 figures

References in corpus (22)

• A nonequilibrium equality for free energy differences
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• The Quantum Jump Approach to Dissipative Dynamics in Quantum Optics
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Fluctuation theorems: Work is not an observable
• Test of Jarzynski and Crooks fluctuation relations in an electronic system
• Experimental Free Energy Surface Reconstruction From Single-Molecule Force Spectroscopy Using Jarzynski's Equality
• Quantum jump approach for work and dissipation in a two-level system
• Distribution of Entropy Production in a Single-Electron Box
• Irreversibility on the Level of Single-Electron Tunneling
• Non-equilibrium Fluctuation Relations in a Quantum Coherent Conductor
• A Quantum Analogue of the Jarzynski Equality
• Unified Treatment of Quantum Fluctuation Theorem and Jarzynski Equality in Terms of microscopic reversibility
• Jarzynski equation for a simple quantum system: Comparing two definitions of work
• Lindblad equation approach for the full counting statistics of work and heat in driven quantum systems
• Work and its fluctuations in a driven quantum system
• Reconstructing the free energy landscape of a polyprotein by single-molecule experiments
• Quantum driving and work
• Equivalence of two Bochkov-Kuzovlev equalities in quantum two-level systems
• Dissipated work and fluctuation relations for non-equilibrium single-electron transitions

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