ABSTRACT Contemporary physics faces an incompatibility between quantum mechanics and GeneralRelativity. The intersection of these models generates theoretical anomalies, notably the vacuum energydensity divergence—the cosmological constant problem—and the violation of unitarity at the event horizonsof black holes. This work presents an analytical derivation of the cosmological constant (Λ) by restructuringthe initial boundary conditions and thermodynamic premises, bypassing the perturbative quantization ofgravity.The proposed model demonstrates that the observable universe operates as a closed dissipativethermodynamic continuum, governed by an equivalence between metric expansion and informationconservation. To formalize this, the derivation requires the reformulation of the quantum vacuum partitionfunction, imposing a holographic restriction on the system's degrees of freedom. By subjugating theEuclidean path integral to the Bekenstein-Hawking bound, the phase space operates in a finite regimedictated by the surface area of the cosmological horizon. This restriction of the phase space prevents thedivergence of the path integral inherent to standard Quantum Field Theory. Applying the Cohen-Kaplan-Nelson formulation, the ultraviolet cutoff obeys the infrared scale, establishing an analytical limit for thevacuum energy density. The macroscopic vacuum acts through a pressure vector associated with geometricdilation. The application of the First Law of Thermodynamics occurs through the heat flow and the workperformed on the horizon, overcoming the algebraic flaw of zeroing the variation of the volumetric internalenergy. Applying Jacobson's formalization, the energy flow through the membrane is related to thetemperature and to the variation of the local informational entropy. During metric expansion, the mechanicalwork executed by the vacuum pressure in dilating the volume equates to this energy flow. Consequently, thecosmological constant is isolated analytically and derived as the mechanical and thermodynamic costrequired to accommodate the continuous exhaustion of the system's degrees of freedom. Isolating thecosmological constant Λ, the variable is redefined under the scope of gravitational thermodynamics: Λ = (8π G T / c⁴) (dS / dV)The cosmological constant Λ acts as a function of the rate of variation of theinformational entropy per unit volume (dS/dV), multiplied by the thermal temperature of the horizon (T). Thisthermodynamic mechanics simultaneously resolves the black hole information paradox. The horizonfunctions as a localized node of informational saturation where quantum states remain encoded on thetopological membrane and are re-emitted via Hawking radiation, grounding the cosmological model on theconservation of information.KEYWORDS: Informational Cosmology; Quantum Thermodynamics; Emergent Gravity; Universal Equationof State; Information Paradox; Dark Matter; CPT Symmetry.
André Luis Alves DeLemos (Thu,) studied this question.