Calculating work in weakly driven quantum master equations: backward and forward equations

Abstract

I present a technical report indicating that the two methods used for calculating characteristic functions for the work distribution in weakly driven quantum master equations are equivalent. One involves applying the notion of quantum jump trajectory [Phys. Rev. E 89, 042122 (2014)], while the other is based on two energy measurements on the combined system and reservoir [Silaev, et al., Phys. Rev. E 90, 022103 (2014)]. These represent backward and forward methods, respectively, which adopt a very similar approach to that of the Kolmogorov backward and forward equations used in classical stochastic theory. The microscopic basis for the former method is also clarified. In addition, a previously unnoticed equality related to the heat is also revealed.

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References in corpus (16)

• Fluctuation theorems: Work is not an observable
• Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System
• Markovian Master Equations: A Critical Study
• Comparison of far-from-equilibrium work relations
• Non-equilibrium quantum fluctuations of work
• Quantum Operation Time Reversal
• Fluctuation theorems in driven open quantum systems
• Quantum work relations and response theory
• The quantum-classical correspondence principle for work distributions
• Lindblad equation approach for the full counting statistics of work and heat in driven quantum systems
• Moments of work in the two-point measurement protocol for a driven open quantum system
• Equivalence of two Bochkov-Kuzovlev equalities in quantum two-level systems
• Calculating work in adiabatic two-level quantum Markovian master equations: A characteristic function method
• Fluctuations of work in nearly adiabatically driven open quantum systems
• Quantum fluctuation theorem: Can we go from micro to meso?
• Nonequilibrium work equalities in isolated quantum systems

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• Quantum Trajectory Thermodynamics with Discrete Feedback Control
• Characteristic Functions Based on Quantum Jump Trajectory
• Quantum Fluctuation Theorems
• Quantum jump model for a system with a finite-size environment
• Joint statistics of work and entropy production along quantum trajectories
• Quantum Fluctuation Theorem under Continuous Measurement and Feedback
• Work Distributions in 1-D Fermions and Bosons with Dual Contact Interactions
• Comparison between quantum jumps and master equation in the presence of a finite environment
• Calorimetric measurement of work for a driven harmonic oscillator
• Quantum thermodynamics under continuous monitoring: a general framework