What is the most general class of quasiprobabilities of work?

TL;DR

This paper investigates the most general form of quasiprobabilities of work in quantum thermodynamics, establishing a foundational framework and exploring their properties including contextuality.

Contribution

It introduces a general notion of quasiprobability of work based on fundamental conditions, extending the analogy to Gleason's theorem, and analyzes their contextuality.

Findings

Defines the most general quasiprobability of work satisfying key conditions

Establishes a framework analogous to Gleason's theorem for quasiprobabilities

Discusses the contextuality inherent in the quasiprobability protocol

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.