Applying Jacobson's thermodynamic derivation to general non-Riemannian spacetimes selects a unique Einstein-Hilbert-plus-torsion-vector-squared theory in the torsion-only case, and yields no action-based theory when non-metricity is present.
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Jacobson's thermodynamic approach to classical gravity applied to non-Riemannian geometries: remarks on the simplicity of Nature
Applying Jacobson's thermodynamic derivation to general non-Riemannian spacetimes selects a unique Einstein-Hilbert-plus-torsion-vector-squared theory in the torsion-only case, and yields no action-based theory when non-metricity is present.