Information--Driven Dynamics of the Universe: A Renormalizable Unified Entanglement--Entropy Quantum Field Theory

This work presents the formulation of a Renormalizable Unified Entanglement–Entropy Quantum Field Theory (RUEQFT), where time-like and space-like entropy couplings (λt,,λx) emerge as marginal operators in the Schwinger–Keldysh action, leading to anisotropic critical dynamics. We derive a universal mass–damping relation for pseudo–Goldstone modes, Ω=Cm2+Δη, with Δη=ηt−ηx, unifying mass, damping rate, and entropy production under a single scaling framework.

Through real-time functional renormalization group (FRG) analysis of the critical O(4) model, we find Δη∗=0.018(4), predicting a ∼10% excess damping over classical hydrodynamics near the QCD chiral critical point. Phenomenological implications are discussed for heavy-ion collisions, high-Tc superconductors, charge-density wave materials, and cold-atom quantum simulators—all of which offer experimentally testable predictions.

The theory introduces an "information–Lorentz factor" γth=ξΔη, which generalizes dynamical scaling laws and may connect to ideas in entropic gravity and holography.

Keywords: Entanglement entropy, pseudo-Goldstone damping, Δη, information thermodynamics, QCD critical point, RUEQFT