The Thermodynamic Cost of Wave-Particle Duality: Directional Dephasing in Interferometry

Wave–particle duality in interferometric systems is commonly formulated through complementarity relations linking fringe visibility and path distinguishability. In realistic experiments, interference suppression arises not only from unitary which-path marking but also from environment-induced decoherence. We derive an angle-dependent pure-dephasing model from a microscopic system–bath Hamiltonian, obtaining a Lindblad master equation with geometric coupling dependence. Moving beyond the Markovian limit, we utilize a second- order time-convolutionless (TCL2) expansion with a structured spectral density to show that geometric scaling persists in non-Markovian regimes, potentially leading to geometry-dependent coherence revivals. Furthermore, we explicitly derive the entropy production rate, demonstrating that the transition toward classicality is quantitatively governed by directional entropy flow. The framework remains fully within standard quantum mechanics, introducing no modifications to the Schr¨odinger equation. Experimental falsifiability criteria, including early-time scaling and coherence revivals, are presented.