Disordered nonlinear systems have long been central to studies of complex dynamical behavior, yet most studies focus on spatial randomness. In contrast, when disorder fluctuates temporally, it drives the system far from equilibrium, giving rise to fundamentally different dynamical behaviors. Here, we investigate a nonlinear dispersive system subject to correlated temporal disorder, revealing how the interplay between dispersion and temporal disorder reshapes its dynamical phases. By analyzing correlation dynamics and replica-overlap statistics, we identify a transition from ergodic to nonergodic clustering, marked by distinct correlation patterns and symmetry breaking in replica statistics. These results clarify the statistical mechanics underlying temporally disordered nonlinear waves and provide insight into nonequilibrium phase organization in time-varying photonic systems.

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• Nonlinear optics
• Disordered systems
• Replica methods
• Replica theory