First law of quantum field thermodynamics

We study the notion of work fluctuations in quantum field theory, highlighting that the most common definitions used in finite-dimensional quantum systems cannot be applied to quantum field theory (QFT). Then we propose work distributions that are compatible with QFT, and we show that they satisfy the first law of thermodynamics up to second moments. We also show how these distributions satisfy the Crooks theorem and provide a fully nonperturbative thermodynamic analysis of spacetime localized unitary processes on a quantum field.