Why collective behaviours self-organise to criticality: A primer on information-theoretic and thermodynamic utility measures

Abstract

Collective behaviours are frequently observed to self-organise to criticality. Existing proposals to explain these phenomena are fragmented across disciplines and only partially answer the question. This primer compares the underlying, intrinsic, utilities that may explain the self-organisation of collective behaviours near criticality. We focus on information-driven approaches (predictive information, empowerment, and active inference), as well as an approach incorporating both information theory and thermodynamics (thermodynamic efficiency). By interpreting the Ising model as a perception-action loop, we compare how different intrinsic utilities shape collective behaviour and analyse the distinct characteristics that arise when each is optimised. In particular, we highlight that thermodynamic efficiency -- measuring the ratio of predictability gained by the system to its energy costs -- reaches its maximum at the critical regime. Finally, we propose the Principle of Super-efficiency, suggesting that collective behaviours self-organise to the critical regime where optimal efficiency is achieved with respect to the entropy reduction relative to the thermodynamic costs.