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  • Open Access

Memory engine: Self-organized coherence from internal feedback

Aranyak Sarkar*

  • *Contact author: aranyak.sarkar@uni-bayreuth.de, aranyak @barc.gov.in
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Phys. Rev. E 112, 054111 – Published 10 November, 2025

DOI: https://doi.org/10.1103/t7nk-4p57

Abstract

We present a continuous-space realization of the coupled memory graph process, 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 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 memory engine—a self-organizing mechanism converting stored memory into predictive motion—illustrating that coherence arises not from tuning, but from coupling.

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Phys. Rev. E 112, 054111– Published 10 November, 2025
  • Received 20 May 2025
  • Accepted 8 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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