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

Cosmological observations require a small, positive cosmological constant Λ, while con-
ventional quantum field theory predicts a vacuum energy density exceeding the observed
value by many orders of magnitude. We show that this discrepancy—the vacuum catastro-
phe—arises from treating spacetime as a mechanically infinite system, whereas a positive Λ
implies a finite-entropy vacuum governed by horizon thermodynamics. Treating de Sitter
space as a genuine thermodynamic system, we derive the observed vacuum energy density
both from horizon entropy via the Clausius relation and independently from a curvature–
regulated zero-point spectrum. The convergence of these two routes selects a physically
meaningful quantum scale constructed from G, ℏ, c and Λ, which resolves the vacuum catas-
trophe by rendering the vacuum energy finite and radiatively stable without fine tuning.
Within this framework, gravity appears as a thermodynamic response of a finite-entropy
vacuum, and both Newton’s constant and the Principle of Equivalence emerge as conse-
quences of this thermodynamic structure rather than as independent postulates. We further
show that the Planck system, while mechanically complete, is thermodynamically incom-
plete, attaining closure only when Λ is included. The Λ–framework therefore provides a
thermodynamic completion of natural units and a unified description of the quantum and
cosmological vacua.