Quantifying Dissipation from Structure in Active Matter

Active matter systems, driven by non-conservative forces acting on individual particles, show a variety of behaviors and structures not seen in equilibrium systems. However, precisely connecting the structure of active matter to the dissipation of energy is a significant challenge, particularly for systems driven far out of equilibrium. We tackle this problem by developing a perturbative mean field theory that works surprisingly well in predicting structural information even for strongly interacting systems, unlike existing approaches. Significantly, this theory requires no more than the direct correlation function at equilibrium. We show that our approach works well even in moderately driven systems with hard interaction potentials. Then, we extend this theory to develop an expression for the rate of dissipative work and show that a robust relationship with the activity-induced deviation in the correlation function exists. This relationship holds even as the system approaches an activity-induced phase transition very far from equilibrium. Finally, we construct a neural network that maps snapshots of active matter to the energy dissipation encoded in them, consolidating our findings on the connection between static structural information and dissipative work.