  Physical interactions generally respect certain symmetries, such as
reciprocity and energy conservation, which survive in coarse grained isothermal
descriptions. Active many-body systems usually break such symmetries
intrinsically, on the particle level, so that their collective behavior is
often more naturally interpreted as a result of information exchange. Here, we
study numerically how information spreads from a "leader" particle through an
initially aligned flock, described by the Vicsek model without noise. In the
low-speed limit of a static spin lattice, we find purely conductive spreading,
reminiscent of heat transfer. Swarm motility and heterogeneity can break
reciprocity and spin conservation. But what seems more consequential for the
swarm response is that the dispersion relation acquires a significant
convective contribution along the leader's direction of motion.
