Non-Perturbative Renormalization Group of the Information Dissipation Tensor

Abstract

The non-perturbative self-coupling of the information dissipation tensor gives rise to a fundamentally new dynamical equilibrium mechanism — a self-limitation between quantum fluctuations and classical dissipation. Starting from the quantum field-theoretic foundations of the Order Parameter Spacetime Theory, this paper derives the non-perturbative renormalization group flow equations for the information dissipation tensor and its feedback coefficients. The core results include: an explicit form of the β-function for the feedback coefficients, which recovers the Schwinger–DeWitt expansion results in the one-loop limit; a proof that when the order-parameter effective mass M → 0, the perturbative divergence is forcibly arrested by the positive-feedback enhancement effect generated by the non-perturbative cubic self-coupling, stabilizing the system at an infrared fixed point; the suppression of the quantum fluctuation power spectrum of the information dissipation tensor near the fixed point, ensuring that the theory returns to the classical regime in the low-energy limit; and, based on the fixed-point structure, a precise determination of the critical value λ_c ≈ 1.6 ± 0.3 and critical exponent θ = 1.59 ± 0.13 for the black hole critical endpoint. The field-theoretic foundation of the Order Parameter Spacetime Theory is thereby elevated from "one-loop validity" to "all-order self-consistency" — the information dissipation tensor is not an external field that needs to be "renormalized", but a self-limiting physical quantity that achieves a quantum-classical dynamical equilibrium through its own nonlinearity.