  According to the Second Law of thermodynamics, the evolution of physical
systems has a preferred direction, that is characterized by some positive
entropy production. Here we propose a direct way to measure the stochastic
entropy produced while driving a quantum open system out of thermal
equilibrium. The driving work is provided by a quantum battery, the system and
the battery forming an autonomous machine. We show that the battery's energy
fluctuations equal work fluctuations and check Jarzynski's equality. Since
these energy fluctuations are measurable, the battery behaves as an embedded
quantum work meter and the machine verifies a generalized fluctuation theorem
involving the information encoded in the battery. Our proposal can be
implemented with state-of-the-art opto-mechanical systems. It paves the way
towards the experimental demonstration of fluctuation theorems in quantum open
systems.
