*3.11. Theorem* ¬(*K* |→ *C*0)

**Proof.** Based on (13) and (19) we can see that {*K*} ⊂ {*C*0}. The *K* principle has rich family of models, so they cannot be contained in a single model for the *C*0 principle. At the level of the model structure, the lack of the considered formal implication is quite clear.

However, let us give two counterexamples of processes that conform to the *K* rule, but not the *C*0 rule. Let it be the ↓→↓ (*Q*<sup>1</sup> − *q*, *W*, *Q*<sup>2</sup> − *q*) engine process with any high efficiency less than 100 % (*q* < *Q*2, *q* ≈ *Q*2) and the ↑ 0 ↑ process heat flow upward (towards higher temperature). These processes are found in the models of *K* principle and do not appear in the model of *C*0 principle. Contrary to appearances, the inverse Carnot cycle (−*Q*1, −*W*, −*Q*2) cannot be added to the engine process in order to obtain a contradictory process ↑ 0 ↑ for these models. This cannot be done because the ultra high efficiency model does not have cooling cycles for *η*˜ = *ηC*. However, when it comes to the ↑ 0 ↑ process, it is possible in separate models that implement the scenario of spontaneous heat flow upward (towards a higher temperature). The Kelvin Principle does not speak of heat reservoirs temperatures, so it should come as no surprise that it determines neither the heat direction nor the Carnot efficiency.
