Work distribution of quantum fields in static curved spacetimes

TL;DR

This work develops a causally consistent framework to define and analyze work distributions for quantum fields in static curved spacetimes by extending the Ramsey interferometry protocol with Unruh-DeWitt detectors. It derives a non-perturbative expression for the characteristic function $\tilde{\mathcal{P}}(\mu)$ of the field and demonstrates that, for thermal $KMS$ states, the forward and reverse work distributions satisfy the Crooks fluctuation theorem and the Jarzynski equality. The analysis includes a detailed treatment of a pointlike detector, yielding compact formulas for the first two moments of the work distribution and recovering the fluctuation-dissipation relation in the high-temperature limit. Overall, the results show that fluctuation theorems persist for quantum fields interacting with localized detectors in static curved spacetimes, connecting relativistic quantum information, thermodynamics, and quantum field theory in curved backgrounds.

Abstract

We investigate the formulation of work distributions for quantum scalar fields in static curved spacetimes by extending the Ramsey interferometric protocol originally developed in previous works for flat spacetimes. The use of Unruh-DeWitt particle detectors provides a causally consistent framework to define and measure work statistics, avoiding the limitations of the two-time projective measurement scheme in relativistic quantum field theory. We derive a non-perturbative expression for the characteristic function of the quantum field and apply it to thermal Kubo-Martin-Schwinger (KMS) states, showing that the resulting work distributions satisfy both the Crooks fluctuation theorem and the Jarzynski equality. Furthermore, we analyse the case of a pointlike detector, obtaining compact expressions for the first two moments of the work distribution, allowing us to recover the standard fluctuation-dissipation relation in the high-temperature limit. Our results demonstrate that fluctuation theorems hold for quantum fields interacting with Unruh-DeWitt particle detectors in static curved spacetimes.