Non-Markovian route to coherence in heterogeneous diffusive systems.

Area of Science:

• Statistical Physics
• Complex Systems
• Active Matter

Background:

• Temporal coherence (persistent alignment) can emerge between agents with distinct dynamics.
• Classical diffusion models struggle with strong heterogeneity and asymmetry in agent dynamics.
• Existing models often require reciprocity or common noise for synchronization.

Purpose of the Study:

• To introduce a novel model, the coupled memory graph process (CMGP), for achieving temporal coherence.
• To demonstrate CMGP's ability to generate synchronized behavior without reciprocity or common noise.
• To explore the phenomenon of 'ghost coherence'—coherence without trajectory convergence—in heterogeneous systems.

Main Methods:

• Development of the coupled memory graph process (CMGP) model.
• Analysis of emergent long-range correlations generated by directed, distance-gated coupling.
• Utilizing Bayesian optimization to identify parameter regions supporting ghost coherence.

Main Results:

• CMGP achieves long-time coherence exceeding inherent memory times, even with mismatched scaling exponents.
• Persistence of coherence arises from emergent correlations within the coupling field, not direct kernel overlap.
• Identified broad parameter regions supporting 'ghost coherence' while preserving distinct agent dynamics.

Conclusions:

• CMGP provides a minimal mechanism for coordination in heterogeneous active systems and viscoelastic environments.
• This mechanism captures synchronization phenomena not explained by standard stochastic models under asymmetry.
• Highlights the importance of emergent correlations in achieving coordinated behavior in complex systems.