I'm investigating the relationship between the WKB (Wentzel–Kramers–Brillouin) approximation and oscillatory sine-cosine dynamics as described in transductive field models, in particular non-equilibrium or open systems.

The WKB approximation typically emerges in quantum mechanics as a semi-classical limit where wavefunction behavior is expressed in terms of exponential or sinusoidal solutions, depending on the energy potential. In recent theoretical approaches, such as those aligning with the Oscillatory Dynamics Transductive-Bridging Theorem (ODTBT), sine and cosine functions are used to represent transductive dynamics between compressed (quantized) and expressive (continuous) phases of physical systems.

In ODTBT, the TWIST is a transductive threshold that links potential and realized states across harmonic fields, and WKB-like formulations (especially in cosmological models) seem to show structural resonance with this logic. I'm curious whether these frameworks have already been explored in depth.

My key questions:

• Can the WKB wavefunction be understood as a localized phase oscillation around a transductive boundary (e.g., TWIST)?
• Has anyone studied WKB-like structures in open/dissipative systems with nonlinear boundary conditions?
• How might thermodynamic irreversibility or entropy gradients influence the interpretation of sine-cosine wave solutions in the WKB context?

I appreciate all references and/or perspectives especially from researchers working on quantum thermodynamics, semiclassical approximations, and transductive field theories.