Entropic Cosmology: Accelerated Expansion of the Universe as Relaxation to the Holographic Attractor ln 2

This paper presents an extended thermodynamic model of gravity that offers a unified mecha-nism for reconciling observational data to solve the fundamental problems of modern cosmol-ogy: the "Vacuum Catastrophe", the "Hubble Tension" (H0), and the "Structure Tension"(S8). Within the framework of the Entropic Relaxation Model (ERM), dark energy istreated not as a static cosmological constant, but as a dynamic pressure arising from thetendency of spacetime to saturate the information capacity of the event horizon.To overcome the limitations of standard holographic models known as Hsu’s Paradox,leading to w = 0, the Interacting Dark Energy (IDE) formalism is applied, fundamen-tally grounded in a Coupled Quintessence Lagrangian. We demonstrate that a non-adiabaticentropy flow (Q > 0) from the matter sector to the vacuum is necessary to generate effectiveacceleration (weff < −1/3). Within this approach, the dark energy density parameter ΩΛevolves toward a fundamental thermodynamic attractor ΩΛ → ln ≈ 0.693.Numerical modeling using the Boltzmann code (CLASS v3.3) confirms that with aninteraction parameter λ ≈ 0.005, the model: 1. Increases the Hubble constant to H0 ≈69.0 km/s/Mpc, reducing the statistical tension from 5σ to an acceptable level of < 2σ; 2.Preserves the age of the Universe at t0 ≈ 13.42 Gyr, which is compatible with the ages ofthe oldest stars; 3. Successfully passes local physics tests (LLR) due to a density screeningmechanism.Finally, we reveal that the phenomenological coupling constant λ coincides with theproduct of the fine-structure constant and the informational bit cost (α ln 2), hinting at adeep connection between dark sector dynamics and quantum electrodynamics.