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.

arXiv comment5 pages. Comments welcome

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• Quantum advantage in batteries for Sachdev-Ye-Kitaev interactions
• Fluctuation theorems for genuine quantum mechanical regimes
• Quantum unital Otto heat engines: using Kirkwood-Dirac quasi-probability for the engine's coherence to stay alive
• Role of quantum correlations in daemonic expected utility
• A Wigner quasiprobability distribution of work
• Quasiprobability distributions with weak measurements
• Energy densities in quantum mechanics
• Excited stated quantum phase transitions and the entropy of the work distribution in the anharmonic Lipkin-Meshkov-Glick model
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• Quantum advantage from negativity of a work quasiprobability distribution