A Non-Markovian Route to Coherence in Heterogeneous Diffusive Systems

TL;DR

This paper introduces the Coupled Memory Graph Process (CMGP), a novel model demonstrating how agents with different dynamics can achieve temporal coherence through internal memory and directed coupling, surpassing classical diffusion models.

Contribution

The paper presents the CMGP model, revealing a minimal mechanism for emergent coordination in heterogeneous diffusive systems that classical models cannot capture.

Findings

Active particles with long-range memory can synchronize with subdiffusive partners.

Bayesian optimization identifies parameter regimes supporting ghost coherence.

The mechanism applies to viscoelastic environments and heterogeneous active 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.