Structural Asymmetry in Finite Systems: Geometry-Induced Negative Drift
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| Format: | Recurso digital |
| Langue: | anglais |
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Zenodo
2026
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| _version_ | 1866901785911754752 |
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| author | Minh, Ho |
| author_facet | Minh, Ho |
| contents | <p>This work introduces the Structural Asymmetry Principle, a minimal, model-independent framework explaining why instability and negative drift arise generically in finite systems.</p> <p>We show that when structured states occupy a vanishing fraction of the state space, stochastic dynamics induce an inherent asymmetry in transitions: trajectories are more likely to leave structured regions than to return to them. Under mild conditions, this leads to a strictly negative long-run expectation.</p> <p>The result does not rely on entropy, specific mechanisms, or domain-dependent assumptions. Instead, it follows directly from geometric sparsity and ergodic exploration. Consequently, stability is not a generic outcome but requires sustained compensation.</p> <p>This formulation provides a unified structural explanation for instability across domains, including stochastic processes, learning systems, and decision dynamics.</p> <p>Technical proofs are provided in the Appendix.</p> <p>Stability is non-generic in finite systems and requires sustained compensation.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19582028 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Structural Asymmetry in Finite Systems: Geometry-Induced Negative Drift Minh, Ho structural asymmetry negative drift finite systems stochastic dynamics Markov chains ergodicity geometric sparsity stability non-equilibrium systems long-run behavior system dynamics decision processes <p>This work introduces the Structural Asymmetry Principle, a minimal, model-independent framework explaining why instability and negative drift arise generically in finite systems.</p> <p>We show that when structured states occupy a vanishing fraction of the state space, stochastic dynamics induce an inherent asymmetry in transitions: trajectories are more likely to leave structured regions than to return to them. Under mild conditions, this leads to a strictly negative long-run expectation.</p> <p>The result does not rely on entropy, specific mechanisms, or domain-dependent assumptions. Instead, it follows directly from geometric sparsity and ergodic exploration. Consequently, stability is not a generic outcome but requires sustained compensation.</p> <p>This formulation provides a unified structural explanation for instability across domains, including stochastic processes, learning systems, and decision dynamics.</p> <p>Technical proofs are provided in the Appendix.</p> <p>Stability is non-generic in finite systems and requires sustained compensation.</p> |
| title | Structural Asymmetry in Finite Systems: Geometry-Induced Negative Drift |
| topic | structural asymmetry negative drift finite systems stochastic dynamics Markov chains ergodicity geometric sparsity stability non-equilibrium systems long-run behavior system dynamics decision processes |
| url | https://doi.org/10.5281/zenodo.19582028 |