Mathematical Implications of Non-Homogeneous Para-Topological Convergences Between Orthogonal Unbridged n-Spaces IV Thermodynamic and Dynamical Stability of Non-Homogeneous Para-Topological Crossings

Developed is an effective mathematical framework for a hypothetical crossing between twootherwise orthogonal, non-bridged (n)-dimensional spaces. The crossing is represented by alocalized interaction kernel with finite radial extent and finite transverse thickness. Demonstrated isthe process of a crossing model of two n-dimensional universes with the same dimension anddiscussed are several physical phenomena in this context like entropy-flux, thermodynamiccoupling, geometry influence between the two universes . Introduced is an effective entropy-transfer channel between the two sectors. The analysis demonstrates that strong geometric screeningcan suppress thermodynamic exchange without requiring complete geometric decoupling. Furtherexplored is the stability of this crossing system, its time dependent tachyon state and analyzed isthe geometric screening, which couples to interaction of entropy and thermodynamic conditions ofthe two universes.