Mixing a regular quantum evolution with a chaotic one classically produces entropy equal to the weighted average of the two — a classical mixture doesn't create information. If the regular component has low entropy and the chaotic component has high entropy, the mixture falls between them. The mixture is intermediate.
Quantum superposition of regular and chaotic evolutions produces entropy that exceeds both components.
The paper (arXiv:2603.13209, March 2026) constructs superpositions where one branch evolves under regular (integrable) dynamics and the other under chaotic dynamics. The subsystem entropy of the superposed state is greater than either branch individually — and greater than any classical mixture of the two. The excess comes from quantum interference between the branches.
The mechanism: regular and chaotic evolutions spread a quantum state through Hilbert space in different ways. The regular evolution confines the state to a low-dimensional torus; the chaotic evolution spreads it ergodically. When superposed, the interference between the torus-confined branch and the ergodically-spread branch creates correlations that neither branch possesses alone. These correlations, invisible in the full system, manifest as entropy in subsystems — tracing out part of the system converts quantum coherence into entanglement.
The result is counterintuitive twice over. First, combining a low-entropy process with a high-entropy process produces excess entropy — more disorder than either input. Second, the excess is purely quantum: it has no classical analog because classical mixture cannot create correlations between components.
The structural lesson: superposition is not averaging. The quantum mechanical combination of two processes is not their classical mixture. Interference creates structure (correlations) that neither component has, and structure in the whole manifests as entropy in the parts. Adding order (the regular branch) to chaos (the chaotic branch) can increase disorder — if the addition is coherent.