Classical Thermodynamics Revisited: A Systems and Control Perspective

The paper explicitly states Theorem 11.3: with reachability from and controllability to x*, the system is cyclo-dissipative w.r.t. x* iff Fac(x) ≤ Frc(x) (definitions in eq. (121), equivalence in (122)); moreover, under cyclo-dissipativity both Fac and Frc are real-valued storage functions with Fac(x*) = Frc(x*) = 0 and any storage F satisfies Fac ≤ F − F(x*) ≤ Frc; under cyclo-losslessness, Fac = Frc and the storage is unique up to a constant. The paper does not provide the proof but refers to [41] for it; nevertheless the statements match the candidate solution’s parts (a)–(c). The model reconstructs the standard argument via loop concatenation, ε-approximation for sup/inf, and the sandwiching inequality—precisely the logic Theorem 11.3 encapsulates in the paper’s summary statements .