  In this theoretical study, we determine the maximum amount of work
extractable in finite time by a demon performing continuous measurements on a
quadratic Hamiltonian system subjected to thermal fluctuations, in terms of the
information extracted from the system. This is in contrast to many recent
studies that focus on demons' maximizing the extracted work over received
information, and operate close to equilibrium. The maximum work demon is found
to apply a high-gain continuous feedback using a Kalman-Bucy estimate of the
system state. A simple and concrete electrical implementation of the feedback
protocol is proposed, which allows for analytic expressions of the flows of
energy and entropy inside the demon. This let us show that any implementation
of the demon must necessarily include an external power source, which we prove
both from classical thermodynamics arguments and from a version of Landauer's
memory erasure argument extended to non-equilibrium linear systems.
