Toward variational principles for structure-dynamics coevolution in complex systems

How does organized structure arise from dynamics—and how does it, once formed, reshape the dynamics that sustain it? This question lies at the core of complex systems and remains unresolved. While modern theory provides powerful tools to describe equilibrium, fluctuations, and steady processes, it falls short of explaining how structure and dynamics co-evolve in open, evolving systems. Variational approaches—spanning action principles, stochastic path formulations, information-theoretic methods, and thermodynamic extremal principles—offer a unifying perspective based on selection under constraints. Yet these frameworks remain fragmented, and their domains of validity and connections are not fully understood. This special collection brings these perspectives into dialogue, with the aim of advancing a deeper, more integrated understanding of how complex systems organize, adapt, and evolve.