Non-Markovian route to coherence in heterogeneous diffusive systems

Temporal coherence-persistent alignment across time-can arise between agents with fundamentally distinct dynamics, yet classical diffusion models (Brownian motion, fractional Brownian motion, generalized Langevin equations with shared noise) struggle under strong heterogeneity and asymmetry. We introduce the coupled memory graph process (CMGP), in which internal memory and directed, distance-gated coupling jointly produce synchronized behavior without reciprocity or common noise. Crucially, CMGP exhibits long-time coherence that reaches far beyond typical inherent memory times: an active particle with long-range memory remains temporally coherent with a subdiffusive partner despite mismatched scaling exponents. We show that this persistence arises from emergent long-range correlations generated by the coupling field rather than direct kernel overlap. Using Bayesian optimization, we identify broad parameter regions that support this "ghost coherence" (coherence without trajectory convergence) while preserving distinct exponents. These results outline a minimal mechanism for coordination in heterogeneous active systems and viscoelastic environments-one that standard stochastic models do not capture under comparable asymmetry unless augmented with explicit common drives or symmetric couplings.