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

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Cited by in corpus (10)

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• Fluctuations of work in nearly adiabatically driven open quantum systems
• Optimal control of dissipation and work fluctuations for rapidly driven systems
• Comparison between quantum jumps and master equation in the presence of a finite environment
• Quantum work statistics across a critical point: full crossover from sudden quench to the adiabatic limit
• Testing Time Reversal Symmetry in Artificial Atoms
• Measuring work in quantum many-body systems using a dynamical "work agent"
• Quantum thermodynamics under continuous monitoring: a general framework
• Causality in String Field Theory