# Quantum fluctuation theorems, contextuality and work quasi-probabilities

## TL;DR

This paper explores how quantum contextuality influences fluctuation theorems and work distributions, revealing that negativity in work quasi-probabilities signifies contextuality and connecting classical and quantum measurement schemes.

## Contribution

It demonstrates the link between work quasi-probabilities, contextuality, and measurement schemes, providing a protocol that interpolates between classical and quantum descriptions.

## Key findings

- Negativity of work quasi-probability indicates contextuality.
- Any fluctuation theorem with classical states either admits work quasi-probability or fails with contextual protocols.
- A protocol bridging two-point measurement and weak measurement regimes is proposed.

## Abstract

We discuss the role of contextuality within quantum fluctuation theorems, in the light of a recent no-go result by Perarnau \emph{et al}. We show that any fluctuation theorem reproducing the two-point-measurement scheme for classical states either admits a notion of work quasi-probability or fails to describe protocols exhibiting contextuality. Conversely, we describe a protocol that smoothly interpolates between the two-point measurement work distribution for projective measurements and Allahverdyan's work quasi-probability for weak measurements, and show that the negativity of the latter is a direct signature of contextuality.