On a Thermodynamic Threshold in Emergent Gravity

This paper investigates an emergent-gravity interpretation in which coherent gravitational sourcing manifests only above a critical threshold of an informationally defined collective variable. Below this threshold, the thermodynamic description underlying entropic and holographic derivations of gravity ceases to apply. We formalize a dimensionless emergence parameter Ξ, argue that the associated crossover scale is naturally Planckian, and identify a laboratory threshold near Mc ~ 22 µg within a minimal normalization of the model. A near-threshold scaling ansatz for the effective gravitational coupling is introduced and synthesized with the microscopic entropic-gravity models of Carney et al., yielding quantitative predictions for noise spectra, decoherence rates, and entanglement witnesses. The proposal is formulated as a phenomenological critical-scaling hypothesis whose validity is contingent on an underlying microscopic statistical description, and is falsifiable by tabletop experiments in the 20–60 µg mass range using current or near-term optomechanical and torsion sensor technology.