Identify the quantum‑gravity process constrained by the bulk Tasaki–Crooks fluctuation theorem

Determine the specific quantum‑gravitational process in anti–de Sitter spacetimes that is constrained by the bulk formulation of the Tasaki–Crooks fluctuation theorem derived via the AdS/CFT dictionary, namely the gravitational Schwinger–Keldysh path‑integral representation of the holographic work distribution p(W).

Background

The paper derives a bulk dual of the work distribution p(W) defined by the two‑point measurement on the boundary and formulates the Tasaki–Crooks fluctuation theorem using AdS/CFT. The characteristic functions and partition functions are translated to bulk quantities via gravitational Schwinger–Keldysh path integrals, yielding a holographic prescription for p(W).

The authors argue that this bulk formulation should be viewed as a gravitational fluctuation theorem and is expected to capture mesoscopic aspects of quantum gravity. However, despite computing p(W) and verifying the theorem in a concrete AdS3/BTZ scalar example, they have not yet identified the precise quantum‑gravitational process that the bulk Tasaki–Crooks relation constrains, leaving this as an explicit task for future work.