A time-work uncertainty relation in quantum systems

TL;DR

This paper explores a time-work uncertainty relation in quantum systems, proposing that work defined via energy measurements obeys an uncertainty principle in both closed and weakly open quantum systems.

Contribution

It introduces a novel uncertainty relation for quantum work based on energy measurements, extending the concept to open systems.

Findings

Work obeys a time-work uncertainty relation in closed quantum systems.

The relation also holds for weakly coupled open quantum systems.

Provides theoretical foundation for quantum thermodynamics uncertainty principles.

Abstract

In quantum systems, a plausible definition of work is based on two energy measurement scheme. Considering that energy change of quantum system obeys a time-energy uncertainty relation, it shall be interesting to see whether such type of work as well obeys an analogous uncertainty relation. In this note I argue that this relation indeed exists for closed quantum systems and open quantum systems, which the latter are assumed to be weakly coupled with their environments.