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

TL;DR

This paper compares various information-theoretic and thermodynamic utility measures to explain why collective behaviors tend to self-organize at criticality, highlighting thermodynamic efficiency as a key factor.

Contribution

It introduces a unified analysis of intrinsic utilities, especially thermodynamic efficiency, in explaining self-organization at criticality using the Ising model as a perception-action loop.

Findings

Thermodynamic efficiency peaks at criticality.

Different utilities influence collective behavior characteristics.

Proposes the Principle of Super-efficiency for self-organization.

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.