Topological Bifurcation in Fluid Dynamics: An H3QM Analysis of the Ranque-Hilsch Vortex Tube

The Ranque-Hilsch Vortex Tube (RHVT), often described as a mechanical "Maxwell's Demon", represents a profound challenge in fluid dynamics. It separates a single compressed gas stream into distinct hot and cold flows without any moving parts. Historically, modeling this energy separation has heavily relied on complex, continuous Navier-Stokes equations and computationally expensive Computational Fluid Dynamics (CFD). This paper proposes a novel explanatory framework based on the "Discrete Duality Theory" of Holographic 3D Quantum Mechanics (H3QM). Instead of calculating absolute continuous trajectories in phase space, H3QM maps the high-energy fluid into a discrete topological network. We demonstrate that the tangential injection of compressed gas acts as a massive geometric phase rotation operator. This phase shift induces a topological bifurcation, tearing the probability flow of the network and forcing the system into two distinct topological attractors: an outer high-phase/low-tension attractor (hot flow) and an inner tension-collapsed attractor (cold flow). This discrete Markov Decision Process (MDP) paradigm provides an elegant and computationally efficient alternative for modeling thermodynamic separation phenomena, replacing traditional continuous calculus. Furthermore, we define the exact temperature via stationary distribution and propose the "Topological Heat Density Constant" (ρH3QMρH3QM) as a quantized boundary for thermodynamics. (Note: This publication includes three identical manuscript versions in English [en-US], Traditional Chinese [zh-TW], and Simplified Chinese [zh-CN] to facilitate global academic exchange.)