The Tenson Limit Equation and the Unified Entropy Flow: Toward a Tensorial Formulation of Non-Equilibrium Information Thermodynamics

The Tenson Limit Equation represents the asymptotic extension of the original Tenson Equation, ∇·(????+????????)=0, integrating G¨ odel’s incompleteness theorem into a tensorial information–energy frame- work. Through the introduction of the G¨ odel residue term????∞, the system evolves into the form ∇∞·L???? =????∞, where L???? denotes the Tenson Lagrangian field and????∞captures the limit of informational incompleteness. This paper develops the non-equilibrium entropy flow formulation of the Tenson field, providing a concrete tensorial extension ∇???????????????? =????????, which connects entropy flux, production, and the information–energy balance in dynamic open systems.