Information-Thermodynamic Tensor Networks and Nonequilibrium Collapse Dynamics — Emergence of Macroscopic Effective Constants and Critical Phenomena via Coarse-Graining of Cognitive Projections —

This paper proposes a phenomenological framework that integrates the physical limits of microscopic information processing (metabolic constraints) with macroscopic nonequilibrium dynamics in complex network systems. While conventional models often focus on optimizing the "content" (information and algorithms), this study provides a structural anatomy of the "container" (the physical and cognitive hardware of nodes). <strong>Disclaimer:</strong> <em>This paper does not aim to provide a rigorous formal proof from the first principles of pure mathematics or theoretical physics. Rather, it employs mathematical concepts as an engineering blueprint to perform a "structural calculation" of the physical limits of macroscopic governance and organizational hardware.</em> By defining an "effective dissipation functional" based on Landauer's limit, we formulate an information-geometric coarse-graining rule based on the minimization of Kullback-Leibler divergence loss. Furthermore, we present a mathematical scenario using the Renormalization Group (RG) flow to illustrate how macroscopic effective constants (nonlinear dissipation exponent, spatial impedance, and macroscopic rigidity) emerge endogenously as scale-invariant universality classes. This structural model redefines macroscopic phenomena such as functional failures in information networks as universal phase transitions and cascading critical phenomena, providing a physical rationale for the inevitable thermodynamic collapse of highly complex systems.