Why collective behaviours self-organize to criticality: a primer on information-theoretic and thermodynamic utility measures.

Collective behaviours are frequently observed to self-organize to criticality. Existing proposals to explain these phenomena are fragmented across disciplines and only partially answer the question. This primer compares the underlying, , utilities that may explain the self-organization 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 optimized. 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 , suggesting that collective behaviours self-organize to the critical regime where optimal efficiency is achieved with respect to the entropy reduction relative to the thermodynamic costs.