Cosmological constant as horizon thermodynamic equilibrium: a free-energy derivation

We derive the cosmological constant from a thermodynamic equilibrium condition on the vacuum free energy Φ = u − T s. The vacuum free-energy eld ϕ is treated as a non-dynamical thermodynamic order parameter whose value is xed by the GibbonsHawking horizon boundary condition, rather than as a propagating scalar degree of freedom. A near-cancellation between vacuum energy and horizon entropy yields a residual free-energy density that scales as Λ ∼ 1/RH2, where RH is the cosmological horizon radius. Because ϕ carries nokinetic term and no propagating modes, the eective potential is immune to ultraviolet radiative correctionsresolving the quantum-stability objection that undermines conventional scalar-eld approaches to the cosmological constant. The framework reproduces the observed value Λ ≈ 10−52 m−2 and predicts a slowly evolving dark-energy component. We derive a present-day equation of state w0 ≈ −0.83, consistent with recent dynamical dark-energy hints from DESI baryon acoustic oscillation data.