The Memory Engine: Self-Organized Coherence from Internal Feedback

TL;DR

This paper introduces a self-organized memory engine where internal feedback in a viscoelastic system leads to emergent coherent motion, transitioning from diffusion to structured, phase-locked dynamics without external forces.

Contribution

It presents a continuous-space model of a memory-driven coherence mechanism, demonstrating how internal feedback induces structured motion and phase-locking in a minimal non-Markovian system.

Findings

Transition from diffusion to burst-trap cycles controlled by substrate stiffness

Multimodal speed distributions and directional locking observed

Coherence aligns with memory energy saturation and spectral entrainment

Abstract

We present a continuous-space realization of the Coupled Memory Graph Process (CMGP), a minimal non-Markovian framework in which coherence emerges through internal feedback. A single Brownian particle evolves on a viscoelastic substrate that records its trajectory as a scalar memory field and exerts local forces via the gradient $\nabla$ of accumulated imprints. This autonomous, closed-loop dynamics generates structured, phase-locked motion without external forcing. The system is governed by coupled integro-differential equations: the memory field evolves as a spatiotemporal convolution of the particle's path, while its velocity responds to the gradient of this evolving field. Simulations reveal a sharp transition from unstructured diffusion to coherent burst-trap cycles, controlled by substrate stiffness and marked by multimodal speed distributions, directional locking, and spectral entrainment. This coherence point aligns across three axes: (i) saturation of memory energy, (ii) peak transfer entropy, and (iii) a bifurcation in transverse stability. We interpret this as the emergence of a \textit{memory engine} -- a self-organizing mechanism converting stored memory into predictive motion -- illustrating that coherence arises not from tuning, but from coupling.