On structural complexity of future colliders

The term complexity, while seemingly intuitive, encompasses a broad range of interacting components governed by local rules. These interactions give rise to nonlinear dynamics, randomness, collective behavior, hierarchical structures, and emergent phenomena. In the context of planning future frontier accelerator-based facilities for nuclear and particle physics, researchers and advisory panels increasingly recognize the growing complexity of large accelerators. This complexity is often associated with a greater number of interconnected systems and components, challenges in design, construction, commissioning, and in achieving optimal operational performance. In this paper, we explore in detail the conceptual, phenomenological, and structural dimensions of complexity in particle accelerators and future colliders. Our analysis is illustrated through a comparative assessment of the complexities associated with several proposed next-generation collider projects.