  We theoretically derive and experimentally compare six different ways to
access entropy production in a cavity QED process. We focus on a bipartite
quantum system under feedback control realizing an autonomous Maxwell's demon
scheme reported by Najera-Santos et al. [Phys. Rev. Research 2, 032025(R)
(2020)], where information encoded in a demon is consumed to transfer heat from
a cold qubit to a hot cavity. By measuring individual quantum trajectories of
the joint demon-cavity-qubit system, we compute the entropy production with six
suggested expressions each using a specific set of trajectories and a specific
data processing. These expressions show different sensitivity to experimental
imperfections as revealed by numerical simulations, allowing to adapt a
particular measurement strategy to specific experimental limitations. Our
results provide a unified view on the various meanings of irreversibility in
quantum systems. They pave the way to the measurement of entropy production
beyond thermal frameworks.
