## 4 Representation and Characterization: Scenarios and States
### S7 Scenario
Finally, we have divided the flat occupancy surface into nine areas as follows:  
1. Low entropy, low energy (blue color);
2. Low entropy, medium energy (light-blue color);
3. Low entropy, high energy (green color);
4. Medium entropy, low energy (illac color);
5. Medium entropy, medium energy (white color);
6. Medium entropy, high energy (pink color);
7. High entropy, low energy (yellow color);  
\begin{table}
\begin{tabular}{l l l l l} \hline
**Sub-Scenario** & **Characterization** & **N.Sub-Scenarios** & **N.States** & **E** & **S** \\ \hline S7\_8 & 3\(\lozenge\)30\(\lozenge\)1 & 30 & 30 \(\times\) (7/3!3!) = 4200 & [12; 30] & [4; 12] \\ \hline S7\_9 & 3\(\lozenge\)20\(\lozenge\)2 & 30 & 30 \(\times\) (7/3!2! 2!) = 6300 & [14;  
From an analytical standpoint, it is evident that the best state is represented by the green area, i.e., Area III, which corresponds to high energy and low entropy. This means that the system under consideration has a fast dynamic that does not create disorder. The two worst areas, for different reasons that we will describe, are Area VII (yellow) and Area IX (red). Area VII (yellow) describes states characterized by low energy and high entropy. This state is the worst if the goal is to bring the system back to a situation of greater equilibrium. In other words, it will be necessary to wait a long time to rebalance the system whose characteristic state falls into the yellow area. Area IX (red) describes states characterized by high energy and high entropy. These are systems characterized by high-speed dynamics close to chaos. The decision-maker will, therefore, have very short decision times, but if the decisions taken are correct, the system, given the high energy, can be rebalanced much more quickly than in the cases falling into Area VII. The last extreme area is Area I (blue), characterized by low energy and low entropy. Since energy is low, the systems represented by states included in the scenarios falling into this area will have very slow dynamics that do not create disorder, as the entropy is very low. In addition to these more extreme areas, we must also consider areas representing more hybrid scenarios. These areas are Area II (light blue), Area IV (lilac), Area VI (pink), and Area VIII (orange). Of these four hybrid areas, the best ones are II and VI, where entropy always has lower  
Figure 2: Allocation of the sub-scenarios S7.# (indicated with only #). Here the different colors represent different area of interest in terms of Entropy and Energy as written above. average values than energy. Less advantageous are the scenarios and states falling into Areas IV and VIII, where entropy is more significant than the system's energy. In particular, Area VIII, except for VII and IX, is the worst of all. Finally, state V (white) is characterized by a complete balance between entropy and energy, with both assuming average values. As we will see later, Areas VII and IX are areas not occupied by admissible states, i.e., states in which the CSFs assume values on a scale of 1-5. Area VII represents low-energy chaos, while IX represents high-energy chaos. Figure 3 shows the table of the sub-scenarios S7_# indicated only by # in the SE plane, i.e., with varying energy and entropy. As you can see, for a given pair (S, E), there can correspond one or more sub-scenarios. From Figure 2, it is evident that some macroscopic states characterized by the pairs (S, E) are not admissible and have been indicated in gray. Specifically, Areas VII and IX do not contain admissible states within them and are, therefore, to be considered as states already out of control because they are chaotic. In relation to the previous figure, in Figure 3 below, we report the level of degeneracy of different ordered pairs (E, S), from which it can be seen that the most degenerate levels occur in the central area of the figure, Area V (white), followed by Areas IV and VI, then II and VII, and finally by VII, IX, III, and I. By the level of degeneracy, we mean the presence of multiple sub-scenarios for the same pair (S, E).