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

## TL;DR

This paper explains how collective behaviors in systems self-organize to a critical state using concepts from information theory and thermodynamics.

## Contribution

The paper introduces the Principle of Super-efficiency to explain why systems self-organize to criticality.

## Key findings

- Thermodynamic efficiency peaks at the critical regime, balancing predictability and energy costs.
- The Ising model helps compare how different utilities influence collective behavior.
- Optimizing intrinsic utilities leads to distinct characteristics in collective systems.

## Abstract

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, intrinsic, 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 Principle of Super-efficiency, 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.