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Work extraction in quantum finite systems is an important issue in quantumthermodynamics. The optimal work extracted is called ergotropy, and it isachieved by maximizing the average work extracted over all the unitary cycles.However, an agent that is non-neutral to risk should extract work by followingthe expected utility hypothesis. Thus, we investigate the optimal workextraction performed by a risk non-neutral agent by maximizing the averageutility function over all the unitary cycles. We mainly focus on initial statesthat are incoherent with respect to the energy basis, achieving a probabilitydistribution of work. In this case we show how the optimal work extraction willbe performed with an incoherent unitary transformation, namely a permutation ofthe energy basis, which depends on the risk aversion of the agent. Furthermore,we also investigate how work extraction is affected by the presence of initialquantum coherence in the energy basis by considering a quasiprobabilitydistribution of work.

Optimal work extraction based on the expected utility hypothesis