A time-work uncertainty relation in quantum systems

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.