## 4 Representation and Characterization: Scenarios and States  
In the previous section, we introduced the set of scenarios. Here, we will summarize the various categories before detailing them. From a mathematical standpoint, the number of possible scenarios is very high; in fact, this number is expressed in terms of permutations with repetition of length 7 from the elements of the set [1,2,3,4,5], and it is, therefore, given using 57, resulting in 78,125 different scenarios. For analytical purposes, it is convenient to cluster the 78,125 scenarios into classes with common properties. Below, we present a statistical clustering to analyze deviations from the fundamental states. In the next section, a more advanced classification in terms of evolutionary dynamics is presented. The clustering of scenarios into classes plays a crucial role. In this modelling phase, clustering scenarios into classes will allow for the deconstruction of information and the construction of analytical and automatic decision support models in the analysis phase. In other words, using a thermodynamic approach, we will show that the 78,125 scenarios can be seen as microscopic states, each of which can be associated with a much lower number of macroscopic states expressed in terms of state variables such as internal energy (E) and entropy (S). The classes of clustered scenarios using statistical techniques will be indicated with the acronym S#, where the symbol # will be a decreasing progressive number starting from seven. Therefore, one scenario will contain multiple seven-component n-tuples. Each seven-component n-tuple describes a state of the system. The components are the seven characteristic CSFs, X\({}_{1}\), X\({}_{2}\), X\({}_{3}\), X\({}_{4}\), X\({}_{5}\), X\({}_{6}\), X\({}_{7}\), which, once assigned, characterize the state of the system under study. Since systems can have different dynamics based on other parameters such as space or time, it might happen that all CSFs vary simultaneously, or only some of them exhibit gradients, while the rest remain in their previously evaluated state. The following Table 1 summarizes the various possibilities. Even though it will be subject to further in-depth analyses, it is interesting to anticipate that there is a connection between the aforementioned scenarios and the type of dynamics of the studied system. Thanks to an in-depth modelling activity to better meet analysis requirements, the seven scenarios mentioned in the following section will be reorganized into twelve. However, the following observations remain valid. Scenario S7 is suitable for describing a system with no memory, meaning that there are no previous observations or it is a system with variable dynamics, where different states are expected with small time or space intervals. Such a scenario is, therefore, a scenario with very high variability from both an energetic and entropic point of view. A priori, it is a scenario that can easily become chaotic. Scenario S6 shows the emergence of persistence, meaning that one of the seven pointers does not change. This means that an order is beginning to emerge; however, variability is still very high, so we are dealing with systems with high informational entropy and tendencies toward chaos. Scenario S5 shows a greater level of order compared to previous cases; in fact, we have two fixed CSFs. However, two fixed CSFs compared to five variables still result in the dominance of variability, instability, and disorder over order. In Scenario S4, we find a slightly unbalanced situation towards disorder, while in S3, order and disorder reverse their roles, meaning that we are dealing with scenarios which contain states with four fixed CSFs and three variables. In other words, in S3, we have a system whose states are more easily predictable; it begins to stabilize over time and takes on a specific characterization. In S2, the situation has only two CSFs that are variable, so we are dealing with systems that express extremely predictable and orderly dynamics.