Gravitational Thermodynamics: How Free Energy Minimization Explains Dark Matter Phenomena

We unify gravity and thermodynamics by letting Newton’s law acquire a density dependent multiplier derived from scalar field free energy minimization. The modified force law is

F(r, ρ) = (G * M1 * M2) / r^2 * (1 + 2 * β^2 * exp(- m_eff(ρ) * r))

where the effective mass comes from the thermodynamic potential

V_eff(ψ) = V(ψ) + ρ * ln(A(ψ)).

This provides a screening based explanation of missing mass, so no dark matter particles are required.

Solar System.
|γ_PPN - 1| < 1e-21 (about 16 orders tighter than Cassini).

Galaxies.
SPARC rotation curves are fit with a single parameter (η ≈ 2).

Clusters.
Bullet Cluster type offsets arise from gas-galaxy differential screening.

Cosmology.
The growth index

γ = 3 * (n + 2) / (2 * (n + 1))

lies in the range 1.5 – 2.25, which allows relief of the H0 tension and earlier structure formation.

The proposal is falsifiable by Euclid weak lensing, CMB-S4, and cluster offset scaling. This thermodynamic gravity framework replaces dark matter with a first principles mechanism.