  We theoretically derive and experimentally compare several different ways to
access entropy production in a quantum process under feedback control. We focus
on a bipartite quantum system 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
distinct expressions derived from different approaches to the system
description and its evolution. Each method uses a specific set of trajectories
and data processing. Our results provide a unified view on the various meanings
of irreversibility in quantum systems and pave the way to the measurement of
entropy production beyond thermal frameworks.
