Self-Organization to the Edge of Ergodicity Breaking in a Complex Adaptive System

TL;DR

This paper introduces EvoSK, a model showing how adaptive systems naturally evolve to a critical state at the boundary of ergodicity breaking, optimizing collective rewards on complex landscapes.

Contribution

It demonstrates that coupled evolutionary dynamics drive systems to a critical ergodic-non-ergodic transition, linking physics of ergodicity breaking to adaptive system optimality.

Findings

System reaches a critical state on the ergodic transition boundary.

System exhibits scale-free avalanches with exponent approximately -1.5.

Collective rewards surpass those of non-evolutionary regimes.

Abstract

Self-organized criticality (SOC) is widely proposed as a fundamental mechanism for collective behavior, yet its role in objective-driven, heterogeneous adaptive systems underpinning real complex systems remains less understood. We introduce EvoSK, a minimal evolutionary model in which agents perform memory dependent reinforcement learning on a rugged Sherrington-Kirkpatrick landscape while the population evolves through extremal replacement of the least fit agents. We demonstrate that this coupled dynamics drives the system to a critical state residing on the transition boundary between ergodic and non-ergodic phases. At this boundary, the system exhibits scale-free evolutionary avalanches with a mean-field exponent $\tau \approx -1.5$, while simultaneously achieving collective rewards that surpass those of any manually finetuned, non-evolutionary regime. Our results provide a mechanistic link between the statistical physics of ergodicity breaking and the functional optimality of complex adaptive systems, suggesting that the edge of ergodicity breaking acts as a robust attractor for systems adapting on rugged, high-dimensional landscapes.