# Work distributions on quantum fields

## TL;DR

This paper introduces a measurement-free work distribution framework for quantum fields, extending quantum thermodynamics concepts to field theory and analyzing work fluctuations in localized processes.

## Contribution

It proposes a new work distribution method for quantum fields that avoids projective measurements and demonstrates its validity through fluctuation theorems and analysis of localized unitaries.

## Key findings

- Work fluctuations increase with process localization in space and time.
- The proposed distribution satisfies Crooks theorem and Jarzynski equality.
- Work distributions depend on temperature and localization degree.

## Abstract

We study the work cost of processes in quantum fields without the need of projective measurements, which are always ill defined in quantum field theory. Inspired by interferometry schemes, we propose a work distribution that generalizes the two-point measurement scheme employed in quantum thermodynamics to the case of quantum fields and avoids the use of projective measurements. The distribution is calculated for local unitary processes performed on Kubo-Martin-Schwinger (thermal) states of scalar fields. Crooks theorem and the Jarzynski equality are shown to be satisfied for a family of spatio-temporally localized unitaries, and some features of the resulting distributions are studied as functions of temperature and the degree of localization of the unitary operation. We show how the work fluctuations become much larger than the average as the process becomes more localized in both time and space.