*3.2. Structure of Models for Clausius I Principle*

The Clausius principle I has a whole family of models, that can be parameterized with the maximum efficiency *η<sup>m</sup>* ∈ [0, 1]:

$$\{\mathbb{C}I\} = \{\mathbb{C}I\}\_{\mathbb{M}} = \{\mathbb{C}I\}0,\\ \{\mathbb{C}I\}\_{0 < \eta\_m < 1},\\ \{\mathbb{C}I\}\_1. \tag{15}$$

We have a separate principle model for each value of maximum efficiency. The principle allows for both a zero efficiency model containing only refrigeration processes without engine processes, and also allows for an efficiency model of 1 (*perpetuum mobile πI I*) without refrigeration processes:

$$\{\Box\}\_0 = \{000, \downarrow 0 \downarrow, 0 \leftarrow \downarrow, \uparrow \leftarrow 0, \downarrow \leftarrow \downarrow, \uparrow \leftarrow \downarrow, \text{ no regimes, } \uparrow \leftarrow \uparrow\},\tag{16}$$

$$\{\{\Box\}\_{0<\eta\_m<1} = \{000, \downarrow 0 \downarrow \downarrow, 0 \leftarrow \downarrow, \uparrow \leftarrow 0, \downarrow \leftarrow \downarrow, \uparrow \leftarrow \downarrow, \uparrow \leftarrow \downarrow\}, \\ \{\downarrow \rightarrow \downarrow\}\_{0<\eta\_m<\eta\_m<1} (\uparrow \leftarrow \uparrow)\_{\eta\_m \le \eta \le 1} \}, \tag{17}$$

$$\{\Box\}\_1 = \{000, \downarrow 0 \downarrow 0 \leftarrow \downarrow, \uparrow \leftarrow 0, \downarrow \leftarrow \downarrow, \uparrow \leftarrow \downarrow, \text{ no } refergators, \downarrow \rightarrow 0, \downarrow \rightarrow \downarrow\}.\tag{18}$$

The first six trivial processes are common to all models, but the engine and refrigeration processes already differ in the sense that in extreme cases one of them does not occur.
