Structural Asymmetry in Finite Systems: Geometry-Induced Negative Drift

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.