  Active systems, which are driven out of equilibrium by local non-conservative
forces, can adopt unique behaviors and configurations. An important challenge
in the design of novel materials which utilize such properties is to precisely
connect the static structure of active systems to the dissipation of energy
induced by the local driving. Here, we use tools from liquid-state theories and
machine learning to take on this challenge. We first demonstrate analytically
for an isotropic active matter system that dissipation and pair correlations
are closely related when driving forces behave like an active temperature. We
then extend a nonequilibrium mean-field framework for predicting these pair
correlations, which unlike most existing approaches is applicable even for
strongly interacting particles and far from equilibrium, to predicting
dissipation in these systems. Based on this theory, we reveal a robust analytic
relation between dissipation and structure which holds even as the system
approaches a nonequilibrium phase transition. Finally, we construct a neural
network which maps static configurations of particles to their dissipation rate
without any prior knowledge of the underlying dynamics. Our results open novel
perspectives on the interplay between dissipation and organization
out-of-equilibrium.
