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 is
treated not as a static cosmological constant, but as a dynamic pressure arising from the
tendency 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-adiabatic
entropy flow (Q > 0) from the matter sector to the vacuum is necessary to generate effective
acceleration (weff < −1/3). Within this approach, the dark energy density parameter ΩΛ
evolves toward a fundamental thermodynamic attractor ΩΛ → ln 2 ≈ 0.693.
Numerical modeling using the Boltzmann code (CLASS v3.3) confirms that with an
interaction 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 of
the oldest stars; 3. Successfully passes local physics tests (LLR) due to a density screening
mechanism.
Finally, we reveal that the phenomenological coupling constant λ coincides with the
product of the fine-structure constant and the informational bit cost (α ln 2), hinting at a
deep connection between dark sector dynamics and quantum electrodynamics.