Construction of a Non-Equilibrium Holographic Principle Theory Based on (∞,2)-category framework

This paper constructs a non-equilibrium holographic principle theory within the (∞,2)-category framework, integrating fractal spacetime geometry, dynamic conformal boundaries, and non-perturbative quantum gravity effects. By introducing fractal spacetime manifolds MF(dH) with dynamically described Hausdorff dimension dH, we establish a categorical correspondence between fractal conformal field theory (CFTF) and bulk spacetime. Key innovations include: 1. Extending the fractal holographic dictionary to revise the duality between boundary operators O(x) and bulk fields ϕ(r,x) into a fractal-dimensiondependent form. 2. An entropy-curvature feedback mechanism unifying non-equilibrium entropy f low with Chern class evolution via fractal thermodynamics and topological entropy production rate σtop. 3. Fractal corrections to black hole information recovery, proposing fractal Page curves and dynamic dark energy generation mechanisms. The theory predicts modified primordial gravitational wave oscillation spectra PT(k) and discrete fractal graviton spectra, testable via LiteBIRD and DECIGO experiments. This research provides a new mathematical framework and observable pathways for quantum gravity, dark energy, and non-equilibrium cosmological evolution.