- **Identify Strengths and Weaknesses (Koopman):** - Strengths: Provides a mathematically rigorous way to linearize non-linear dynamics. Naturally incorporates attractors/stable states as eigenfunctions. Operates on a Hilbert space. - Weaknesses:  ``` HKoopmanHKoopman​ ```  is often infinite-dimensional and abstract (a space of functions on the state space). Making a concrete connection between the inner product  ``` ∣⟨gk∣gψ⟩∣2∣⟨gk​∣gψ​⟩∣2 ```  and the physical probability of transitioning to attractor  ``` SkSk​ ```  requires significant justification and likely depends on how interactions and decoherence are modeled within this framework. It's not immediately obvious if this yields the Born rule naturally. Ensuring the correct symmetries and structure (complex Hilbert space, etc.) is needed.