  Flocking systems are known to be strongly out of equilibrium. Energy input
occurs at the individual level to ensure self-propulsion, and the individual
motility in turn contributes to ordering, enhancing information propagation and
strengthening collective motion. However, even beyond ordering, a crucial
feature of natural aggregations is response. How, then, do off-equilibrium
features affect the response of the system? In this work, we consider a minimal
model of flocking and investigate response behavior under directional
perturbations. We show that equilibrium dynamical fluctuation-dissipation
relations between response and correlations are violated, both at the local and
at the global level. The amount of violation peaks at the ordering transition,
exactly as for the entropy production rate. Entropy is always produced locally
and connected to the local fluctuation-dissipation violation via Harada-Sasa
relationships. However, cooperative mechanisms close to the transition spread
off-equilibrium effects to the whole system, producing an out of equilibrium
response on the global scale. Our findings elucidate the role of activity and
interactions in the cost repartition of collective behavior and explain what
observed in experiments on natural living groups.
