A Thermodynamic Interpretation of the Vacuum Catastrophe via a Λ-Selected Quantum Scale

Cosmological observations require a small, positive cosmological constant Λ, whereasconventional quantum field theory predicts a vacuum energy density exceeding the observedvalue by many orders of magnitude. We demonstrate that this discrepancy—the vacuumcatastrophe—may be traced to treating spacetime as a mechanically infinite system, whilea positive Λ implies a vacuum with finite entropy governed by horizon thermodynamics.Building on Jacobson’s thermodynamic interpretation of the Einstein equations, and treat-ing de Sitter space as a genuine thermodynamic system, we derive the observed vacuumenergy density both from horizon entropy via the Clausius relation and independently froma curvature–regulated zero–point spectrum. The agreement of these two derivations selectsa physically meaningful quantum scale constructed from G, ℏ, c, and Λ, and renders thevacuum energy finite and radiatively stable without requiring fine tuning. Within this frame-work, gravity may be interpreted as a thermodynamic response of a finite–entropy vacuum,and both Newton’s constant and the Principle of Equivalence arise as macroscopic conse-quences of this structure rather than as independent postulates. We further show that thePlanck system, while mechanically complete, is thermodynamically incomplete in the pres-ence of cosmological horizons, attaining thermodynamic closure only when Λ is included.The resulting Λ–framework provides a thermodynamic completion of natural units and aunified description of the quantum and cosmological vacua.