Quantum Bochkov-Kuzovlev Work Fluctuation Theorems

TL;DR

This paper derives quantum fluctuation theorems for work based on the exclusive viewpoint, clarifying differences between various work definitions and providing explicit examples of their distinct statistical behaviors.

Contribution

It introduces a quantum version of the Bochkov-Kuzovlev identity using the exclusive work perspective and compares it with the inclusive approach, clarifying their relations.

Findings

Derived quantum fluctuation theorems for exclusive work

Compared exclusive and inclusive work definitions in quantum systems

Explicit example showing different statistics for $w_0$ and $w_{dis}$

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.