Dark Energy as Residual Vacuum Free Energy: A Thermodynamic Bound on the Cosmological Constant

The cosmological constant problem remains one of the deepest puzzles in theoretical physics: naive quantum field theory estimates of the vacuum energy density exceed the observed value by roughly 120 orders of magnitude. We propose a thermodynamic variational principle that constrains the effective cosmological constant Λeff without fine-tuning. Starting from a free-energy functional Φ[ρ] defined over trial vacuum energy densities and regularised between an ultraviolet cutoff ΛUV and an infrared cutoff set by the Hubble radius H₀⁻¹, the unique minimum of Φ yields a residual vacuum energy density scaling as Λeff ~ H₀²/ln(MPl/H₀). The resulting numerical estimate lies within an order of magnitude of the Planck…