On a Thermodynamic Threshold in Emergent Gravity

This paper introduces the concept of the Thermodynamic Emergence Threshold, an information-theoretic framework proposing that gravitational coupling is an emergent, threshold-dependent phenomenon that only manifests at or above the Planck mass scale (\(M_c \approx 21.8\,\mu\text{g}\)). Rather than quantizing the gravitational field at infinitesimal scales, this model posits that sub-threshold energy densities do not couple to geometry, offering a novel resolution to the cosmological constant vacuum catastrophe. By integrating the entropic gravity frameworks of Verlinde and Jacobson with the open quantum systems approach of Carney et al., the transition is modeled via a modified Lindblad master equation. The paper derives the divergence of the entanglement-to-decoherence ratio near the threshold boundary and frames the running gravitational constant (\(G_{\text{eff}}\)) within concrete universality classes using critical exponent scaling rules. Finally, explicit, falsifiable predictions are provided for near-term microgram-scale tabletop torsion balance experiments and high-frequency (~36 GHz) primordial gravitational wave background observations.