Influence of measurements on the statistics of work performed on a quantum system

The recently demonstrated robustness of fluctuation theorems against measurements [M. Campisi, P. Talkner, and P. Hanggi, Phys. Rev. Lett. 105, 140601 (2010).] does not imply that the probability distributions of nonequilibrium quantities, such as heat and work, remain unaffected. We determine the impact of measurements that are performed during a running force protocol on the characteristic function of work. The results are illustrated by means of the Landau-Zener(-Stuckelberg-Majorana) model. In the limit of continuous measurements the quantum Zeno effect suppresses any unitary dynamics. It is demonstrated that the characteristic function of work is the same as for an adiabatic protocol when the continuously measured quantity coincides with the Hamiltonian governing the unitary dynamics of the system in the absence of measurements.