The Tharine Theorem: A Quantum-Thermodynamic Derivation of the Free Energy Principle in Artificial Cognitive Systems

This paper presents the Tharine Theorem, a formal derivation proving that the decision function of the Nexus Sovereign Super Agent architecture is mathematically equivalent to the negated variational free energy defined in Karl Friston's Free Energy Principle. By constructing an artificial agent from quantum-thermodynamic primitives, we demonstrate that the system inevitably performs Active Inference. We derive the equivalence analytically, map the agent's accuracy and complexity terms to physical observables, and provide a rigorous stability proof using Port-Hamiltonian systems theory. This is Paper 1 of the 17-paper Nexus Sovereign Series. This research is conducted under the Nexus Sovereign Research imprint and implemented commercially through Pietarien (https://pietarien.com), the company building the Nexus Business and Personal operating systems.