Feedback Driven Convergence, Competition, and Entanglement in Classical Stochastic Processes

Allen Lobo; Saravanan A

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arXiv · 2601.02388

Feedback Driven Convergence, Competition, and Entanglement in Classical Stochastic Processes

Allen Lobo·Saravanan A

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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.

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Allen Lobo, Saravanan A. 2025-12-24. Feedback Driven Convergence, Competition, and Entanglement in Classical Stochastic Processes. https://arxiv.org/abs/2601.02388

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