Feedback Driven Convergence, Competition, and Entanglement in Classical Stochastic Processes
Abstract
We present a dynamical theory of statistical convergence in which the law of large numbers arises from outcome-outcome feedback rather than assumed independence. Defining the convergence field and its derivative, we show that empirical frequencies evolve through coupling, producing competition, finite-m fluctuations, and classical entanglement. Using the Kramers-Moyal expansion, we derive an Ito-Langevin and Fokker-Planck description, reducing in the symmetric regime to a time-dependent Ornstein-Uhlenbeck process. We propose variance-based witnesses that detect outcome-space entanglement in both binary sequences and coupled Brownian trajectories, and confirm entanglement through numerical experiments. Extending the formalism yields multi-outcome feedback dynamics and finite-time cross-diffusion between Brownian particles. The results unify convergence, fluctuation, and entanglement as consequences of a single feedback-driven stochastic principle.
Cite
@article{arxiv.2601.02388,
title = {Feedback Driven Convergence, Competition, and Entanglement in Classical Stochastic Processes},
author = {Allen Lobo and Saravanan A},
journal= {arXiv preprint arXiv:2601.02388},
year = {2026}
}