Quantization of the Hubble Flow: Holographic Derivation of Dark Energy in Flux-Driven Cosmologies

Building upon the thermodynamic framework of open cosmological systems previously established Frisina, Zenodo 2026 Paper I & II, we address the Cosmological Constant Problem by combining the Holographic Principle with Non-Equilibrium Thermodynamics. We demonstrate that the vacuum energy density can be derived from first principles by counting the quantum degrees of freedom on the cosmic horizon.Standard Holographic Dark Energy (HDE) models fail to explain the observed stability of the vacuum (w ~ -1) without invoking teleological future horizons. We resolve this impasse by introducing a Flux Injection Term Q(t) originating from the parent vacuum via the Einstein-Rosen bridge. We derive the modified continuity equation where the natural holographic decay due to expansion is compensated by the trans-dimensional energy influx.This identifies Dark Energy not as a static property of space, but as a dynamic equilibrium between geometric expansion (entropy maximization) and external fueling (enthalpy injection), yielding a stable effective cosmological constant compatible with Planck 2018 data and recent DESI 2024 observations suggesting a dynamical equation of state.