  Many biological systems are appropriately viewed as passive inclusions
immersed in an active bath: from proteins on active membranes to microscopic
swimmers confined by boundaries. The non-equilibrium forces exerted by the
active bath on the inclusions or boundaries often regulate function, and such
forces may also be exploited in artificial active materials. Nonetheless, the
general phenomenology of these active forces remains elusive. We show that the
fluctuation spectrum of the active medium, the partitioning of energy as a
function of wavenumber, controls the phenomenology of force generation. We find
that for a narrow, unimodal spectrum, the force exerted by a non-equilibrium
system on two embedded walls depends on the width and the position of the peak
in the fluctuation spectrum, and oscillates between repulsion and attraction as
a function of wall separation. We examine two apparently disparate examples:
the Maritime Casimir effect and recent simulations of active Brownian
particles. A key implication of our work is that important non-equilibrium
interactions are encoded within the fluctuation spectrum. In this sense the
noise becomes the signal.
