Quantum Bochkov-Kuzovlev Work Fluctuation Theorems

Abstract

The quantum version of the Bochkov-Kuzovlev identity is derived on the basis of the appropriate definition of work as the difference of the measured internal energies of a quantum system at the beginning and at the end of an external action on the system given by a prescribed protocol. According to the spirit of the original Bochkov-Kuzovlev approach, we adopt the "exclusive" viewpoint, meaning that the coupling to the external work-source is {\it not} counted as part of the internal energy. The corresponding canonical and microcanonical quantum fluctuation theorems are derived as well, and are compared to the respective theorems obtained within the "inclusive" approach. The relations between the quantum inclusive-work $w$, the exclusive-work $w_0$ and the dissipated-work $w_{dis}$, are discussed and clarified. We show by an explicit example that $w_0$ and $w_{dis}$ are distinct stochastic quantities obeying different statistics.

16 pages

References in corpus (18)

• A nonequilibrium equality for free energy differences
• Fluctuation theorems: Work is not an observable
• Dissipation: The phase-space perspective
• Fluctuation Theorem for Arbitrary Open Quantum Systems
• Fluctuation theorem for currents in open quantum systems
• Comparison of far-from-equilibrium work relations
• Dissipation and lag in irreversible processes
• Fluctuation theorems in driven open quantum systems
• Fluctuation theorems for continuously monitored quantum fluxes
• Quantum work relations and response theory
• Phase Transitions in Small Systems: Microcanonical vs. Canonical Ensembles
• Fluctuation and dissipation of work in a Joule experiment
• Microcanonical quantum fluctuation theorems
• Comparison of work fluctuation relations
• Statistics of work performed on a forced quantum oscillator
• Derivation of Boltzmann Principle
• On a new definition of quantum entropy
• Mechanical Proof of the Second Law of Thermodynamics Based on Volume Entropy

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