Feedback Driven Convergence, Competition, and Entanglement in Classical Stochastic Processes
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908749454639104 |
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| author | Lobo, Allen A, Saravanan |
| author_facet | Lobo, Allen A, Saravanan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02388 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Feedback Driven Convergence, Competition, and Entanglement in Classical Stochastic Processes Lobo, Allen A, Saravanan Statistical Mechanics Data Analysis, Statistics and Probability 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. |
| title | Feedback Driven Convergence, Competition, and Entanglement in Classical Stochastic Processes |
| topic | Statistical Mechanics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2601.02388 |