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

Cosmological observations require a small, positive cosmological constant Λ, whereas
conventional quantum field theory predicts a vacuum energy density exceeding the observed
value by many orders of magnitude. We demonstrate that this discrepancy—the vacuum
catastrophe—may be traced to treating spacetime as a mechanically infinite system, while
a 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 vacuum
energy density both from horizon entropy via the Clausius relation and independently from
a curvature–regulated zero–point spectrum. The agreement of these two derivations selects
a physically meaningful quantum scale constructed from G, ℏ, c, and Λ, and renders the
vacuum 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 the
Planck 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 a
unified description of the quantum and cosmological vacua.