Field-Theoretic and Complex Analytic Modeling of Non-Unitary Information Dissipation in Strained Semiconductor Bottlenecks

We present a rigorous complex analytic and dynamic framework to model information dissipation at hardware bottlenecks within high-throughput application-specific integrated circuits (ASICs). By mapping the electrical and quantum phase states of an electron transport data stream onto a complex manifold C, we demonstrate that pristine data execution is governed by holomorphic flows satisfying the Cauchy-Riemann equations. The injection of hardware security states is driven by hy- perbolic M¨obius transformations within the Special Linear group SL(2, C), inducing a deterministic chaotic boundary with a strictly positive Lyapunov exponent. Finally, we model forced hardware quantization (INT8 truncation) within a 12 nm funnel as a meromorphic singularity. Applying Cauchy’s Residue Theorem, we prove that the non-vanishing contour residue dictates a non-unitary information loss that couples directly to environmental lattice modes, establishing an irreversible physical barrier against side-channel cryptanalysis.