The Leakage Principle: Irreversibility, Structure, and the Emergence of Randomness

We propose the Leakage Principle, a structural principle governing how irreversibility produces complexity, structure, and randomness in dynamical systems and computation. Irreversibility alone does not imply chaos or randomness. When divergence is absent, irreversibility produces symbolic complexity; when symmetry is preserved, it produces stable structure. Randomness emerges only when irreversible information loss becomes untrackable by any finite observer or bounded computation. We demonstrate this principle using a symmetric iterative map exhibiting sharp transitions between ordered, chaotic, and collapsed regimes, and argue that the same mechanism explains limits in computation, pseudorandomness, and complexity theory. These limits are structural rather than technological.