  In a multi-level quantum system Fano coherences stand for the formation of
quantum coherences due to the interaction with the continuum of modes
characterizing an incoherent process. When the incoherent source vanishes, Fano
coherences tend to disappear. In this paper we propose a V-type three-level
quantum system on which we certify the presence of genuinely quantum traits
underlying the generation of Fano coherences. We do this by determining work
conditions that allows for the loss of positivity of the Kirkwood-Dirac
quasiprobability distribution of the stochastic energy variations within the
discrete system. We also show the existence of nonequilibrium regimes where the
generation of Fano coherences leads to a non-negligible amount of extractable
work, however provided the initial state of the discrete system is in a
superposition of the energy eigenbasis. We conclude the paper by studying the
thermodynamic efficiency of the whole process.
