What is the most general class of quasiprobabilities of work?

Abstract: How to give a statistical description of thermodynamics in quantum systems is an open fundamental question. Concerning the work, the presence of initial quantum coherence in the energy basis can give rise to a quasiprobability of work, which can take negative values. Our aim is to identify the most general quasiprobability of work satisfying some fundamental conditions. By doing so, we introduce a general notion of quasiprobability in analogy to the Gleason's theorem. Then, we use these quasiprobabilities to define the quasiprobability of work, and finally we discuss the contextuality of the protocol.