Thermodynamics of Open Cosmological Systems: A Parsimonious Geometric Framework for the Dark Sector and Baryogenesis

We propose a high-energy extension of the ΛCDM model by treating the 4D observable manifold as a brane embedded in an AdS₅ bulk, governed by non-equilibrium thermodynamics. Instead of introducing ad-hoc fields, we show that relaxing the closed-system hypothesis offers a natural resolution to current anomalies. We derive the effective Einstein Field Equations, identifying Dark Matter as the projection of the Bulk Weyl tensor originating from a parallel Shadow Brane, consistent with Bullet Cluster constraints. Furthermore, we address the H₀ tension by modeling Dark Energy as a dynamic injection pressure from a precursor manifold. Finally, we derive the observed Baryon Asymmetry from the Atiyah-Singer Index Theorem applied to the chiral topology of the transfer conduit.