R-layer Mode Theory (RLMT) LIV: Non-equilibrium Information Dynamics of the R-layer

This volume develops the fully nonlinear and non‑equilibrium dynamics of the R-layer, completing the theoretical foundation of the R-layer Mode Theory at the classical level. We construct the modular‑flow geometry, derive nonlinear perturbation theory up to third order, formulate the effective field theory (R‑EFT), and establish the holographic dual description of the R-layer. These results unify information geometry, non‑equilibrium dynamics, and cosmology into a single framework. The initial conditions reconstructed in Volume XLI‑I anchor the theory to observational data, and the predictions derived here provide concrete tests for future experiments. Volume LIV prepares the ground for the quantum R-layer theory developed in Volume LV.