TMDD: Oscillators, Invariants, Boundaries. Part II: Informational Metabolism of the $\theta$-Cell in an Environment

Within the framework of the Tensor Model of Discrete Dynamics (TMDD), a systematic investiga-tion is conducted of the interaction of a θ-cell with its environment. A formalism of informationalmetabolism is introduced a two-stroke process comprising internal restructuring (breathing) anddirected information exchange. Three qualitatively distinct regimes are analyzed depending on theposition of the informational volume V = det(Iˆ) relative to the ontological boundaries Vmin andVmax: (1) moderate exchange far from the boundaries, (2) degradation and activation near Vmin,(3) saturation and creative transition near Vmax. The key role of eective inertia Me(V ) as a dy-namic regulator is demonstrated. Particular attention is paid to the inuence of the environment'sstructure: a coherent environment acts as a teacher and amplier, while an amorphous one acts asa destructuring factor. To describe the interaction of remote cells, the concept of relational distanceRAB is introduced as a fundamental measure of structural dierence, preceding metric space. It isestablished that even in the absence of direct connections, information may be transmitted throughchains of structurally-resonant intermediaries, elegantly solving the problem of "remoteness" in thepre-spatial ontology of TMDD. The results lay the foundation for the transition to systems of manycells, where collective phenomena and emergent spacetime arise.