  Out-of-equilibrium statistical mechanics is attracting considerable interest
due to the recent advances in the control and manipulations of systems at the
quantum level. Recently, an interferometric scheme for the detection of the
characteristic function of the work distribution following a time-dependent
process has been proposed [L. Mazzola {\it et al}, Phys. Rev. Lett. {\bf 110}
230602 (2013)]. There, it was demonstrated that the work statistics of a
quantum system undergoing a process can be reconstructed by effectively mapping
the characteristic function of work on the state of an ancillary qubit. Here,
we expand that work in two important directions. We first apply the protocol to
an interesting specific physical example consisting of a superconducting qubit
dispersively coupled to the field of a microwave resonator, thus enlarging the
class of situations for which our scheme would be key in the task highlighted
above. We then account for the interaction of the system with an additional one
(which might embody an environment), and generalise the protocol accordingly.
