In this article we introduce a quasiprobability distribution of work that is
based on the Wigner function. This construction rests on the idea that the work
done on an isolated system can be coherently measured by coupling the system to
a quantum measurement apparatus. In this way, a quasiprobability distribution
of work can be defined in terms of the Wigner function of the apparatus. This
quasidistribution contains the information of the work statistics and also
holds a clear operational definition. Moreover, it is shown that the presence
of quantum coherence in the energy eigenbasis is related with the appearance of
characteristics related to non-classicality in the Wigner function such as
negativity and interference fringes. On the other hand, from this
quasiprobability distribution it is straightforward to obtain the standard
two-point measurement probability distribution of work and also the difference
in average energy for initial states with coherences.Comment: 11 pages, 3 figure