Non-Equilibrium Thermodynamics in Energy-Efficiency Theory: Entropy Production and Yang's Energy Ratio

Energy-Efficiency Theory (EET) provides a first-principles ontology of energy allocation. Here we reformulate the core laws of non-equilibrium thermodynamics within the EET framework, establishing a mapping between classical thermodynamic quantities and the EET energy parameters Ė_main, Ė_resp, and Yang's energy ratio η = Ė_resp / Ė_main. The system is assumed to be in thermal contact with a reservoir at temperature T. We postulate that the resonance state η = 1 minimizes the entropy production rate. Expanding Ṡ_prod around η = 1 yields the universal scaling Ṡ_prod(η) = Ṡ_min + K(1-η)^2, analogous to the Landau expansion for critical phenomena. The framework is compatible with Onsager's reciprocal relations and the fluctuation-dissipation theorem. We propose an experimentally falsifiable prediction using a thermoelectric module (e.g., Bi2Te3), where the total entropy production as a function of the external voltage V (which tunes η) is predicted to exhibit a distinct parabolic minimum at η = 1, deviating from the classical constant-coefficient baseline. This work establishes the thermodynamic foundation of EET, bridging its axiomatic core with measurable non-equilibrium phenomena.