A Non-Markovian Route to Coherence in Heterogeneous Diffusive Systems

Abstract: Temporal coherence-persistent alignment across time-can arise between agents with fundamentally distinct dynamics, a behavior that classical diffusion models (e.g., Brownian motion, fractional Brownian motion, generalized Langevin equation) are inherently limited in capturing, particularly under strong heterogeneity. We introduce the Coupled Memory Graph Process (CMGP), where dynamic interplay between internal memory and directed coupling enables synchronized behavior even in the absence of reciprocity. An active particle with long-range memory remains temporally coherent with a subdiffusive partner, despite mismatched scaling laws and asymmetric information flow. Bayesian optimization identifies a broad parameter regime supporting this phenomenon, characterized by a high State Persistence Index SPI. These results uncover a minimal mechanism for emergent coordination-a form of ghost coherence-that remains inaccessible to classical stochastic models, with implications for viscoelastic environments and heterogeneous active systems.