This work introduces the Structural Asymmetry Principle, a minimal, model-independent framework explaining why instability and negative drift arise generically in finite systems. 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. 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. This formulation provides a unified structural explanation for instability across domains, including stochastic processes, learning systems, and decision dynamics. Technical proofs are provided in the Appendix. Stability is non-generic in finite systems and requires sustained compensation.
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Ho Minh
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Ho Minh (Tue,) studied this question.
www.synapsesocial.com/papers/69e07d1d2f7e8953b7cbe2ef — DOI: https://doi.org/10.5281/zenodo.19582028