Self-Organization to the Edge of Ergodicity Breaking in a Complex Adaptive System
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908973558398976 |
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| author | Lesmana, Nixie Sapphira Feng, Ling Chen, Kan Lai, Choy Heng |
| author_facet | Lesmana, Nixie Sapphira Feng, Ling Chen, Kan Lai, Choy Heng |
| contents | 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 $τ\approx -1.5$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15669 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Self-Organization to the Edge of Ergodicity Breaking in a Complex Adaptive System Lesmana, Nixie Sapphira Feng, Ling Chen, Kan Lai, Choy Heng Adaptation and Self-Organizing Systems 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 $τ\approx -1.5$, 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. |
| title | Self-Organization to the Edge of Ergodicity Breaking in a Complex Adaptive System |
| topic | Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2604.15669 |