Thermodynamic-Brane Cosmology: The Q-Rubin Hypothesis v2.0 (Distributed Field Formulation).

We extend the Q-Rubin cosmological hypothesis from a localized brane-bulk energy-exchange picture (v1.0) to a distributed-field formulation (v2.0). The causal agent of late-time energy transfer still originates at the brane boundary, but its influence is modeled by a covariant interaction four-current J^μ that permeates the brane and couples to an emergent, coarse-grained field Φ_Q. This preserves local conservation of total stress-energy, keeps early-universe physics intact, and yields testable late-time signatures in the expansion history, structure growth, and CMB spectral distortions while respecting CMB/BBN and GW speed constraints [1, 2, 3].