  Time-reversal symmetry breaking and entropy production are universal features
of nonequilibrium phenomena. Despite its importance in the physics of active
and living systems, the entropy production of systems with many degrees of
freedom has remained of little practical significance because the
high-dimensionality of their state space makes it difficult to measure. Here we
introduce a local measure of entropy production and a numerical protocol to
estimate it. We establish a connection between the entropy production and
extractability of work in a given region of the system and show how this
quantity depends crucially on the degrees of freedom being tracked. We validate
our approach in theory, simulation, and experiments by considering systems of
active Brownian particles undergoing motility induced phase separation, as well
as active Brownian particles and E. Coli in a rectifying device in which the
time-reversal asymmetry of the particle dynamics couples to spatial asymmetry
to reveal its effects on a macroscopic scale.
