  Because of its nonequilibrium character, active matter in a steady state can
drive engines that autonomously deliver work against a constant mechanical
force or torque. As a generic model for such an engine, we consider systems
that contain one or several active components and a single passive one that is
asymmetric in its geometrical shape or its interactions. Generally, one expects
that such an asymmetry leads to a persistent, directed current in the passive
component, which can be used for the extraction of work. We validate this
expectation for a minimal model consisting of an active and a passive particle
on a one-dimensional lattice. It leads us to identify thermodynamically
consistent measures for the efficiency of the conversion of isotropic activity
to directed work. For systems with continuous degrees of freedom, work cannot
be extracted using a one-dimensional geometry under quite general conditions.
In contrast, we put forward two-dimensional shapes of a movable passive
obstacle that are best suited for the extraction of work, which we compare with
analytical results for an idealised work-extraction mechanism. For a setting
with many noninteracting active particles, we use a mean-field approach to
calculate the power and the efficiency, which we validate by simulations.
Surprisingly, this approach reveals that the interaction with the passive
obstacle can mediate cooperativity between otherwise noninteracting active
particles, which enhances the extracted power per active particle
significantly.
