*2.2.4. Description of some specific syzygies*

To include more details on the approach presented before and the characteristics of the KP (*K*(*i*) ) a set of syzygies is illustrated for the case of NES, as follows [7]:

	- **◦** It conserves only when all the processes of the system/environment are reversible
	- **◦** It is destroyed when the process is irreversible

An illustration of these characteristics is shown in Figure 2.

In Figure 2, the transition matrix may be considered an isomorphic relationship for the aspects considered above. This matrix is actually a function of the considered categories [4]—defined in the KP structure of type*K***(***i***)** for each source of energy and phase in which the sources may be at a certain stage of changes, as a development of the approaches from [1–6, 11].

Every phase of a NES and every emergent phase are composed of (Figure 3):


where *k* = 0, 1, 2, 3; *i* = 1, 2, 3, *si j* = 1,…9.

Some Considerations on the Lessons Learnt from the Cavalcade of Changes in Physics' Models http://dx.doi.org/10.5772/65414 49

**Figure 2.** Transition matrix for energy sources and levels of NES example [11]

*2.2.4. Description of some specific syzygies*

in the Knowledge Society

(*K*(*i*)

48

erties.

To include more details on the approach presented before and the characteristics of the KP

Proceedings of the International Conference on Interdisciplinary Studies (ICIS 2016) - Interdisciplinarity and Creativity

**•** Exergy (Ex) for an NES (defined as the maximum work possible for a process that brings the system to equilibrium with a heat reservoir) as a measure of the process of energy

**◦** It conserves only when all the processes of the system/environment are reversible

**•** Synergy (Sy) as a measure of a set of NES that appear from the existence and interaction all its systems and components, leading to a new set of more characteristics for NES as a whole

**•** Emergence (Em) from one level to another (for example, from SQ to CSU) as a process in which the entities, patterns, and regularities/irregularities are generated by interactions between smaller (or from lower level) entities, which do not have themselves those prop‐

**•** Nonlinearity (even for simple systems) and/or complexity (NlnCx) for a NES as a source of

**•** The features of a SAC considering fractals (Fr) are defined starting from the characteristics of such systems. In the NES example and its KP structures of *K*(*i*) type, as topological structures of the knowledge gained for a given system at a given level, the fractal behaviors

In Figure 2, the transition matrix may be considered an isomorphic relationship for the aspects considered above. This matrix is actually a function of the considered categories [4]—defined in the KP structure of type*K***(***i***)** for each source of energy and phase in which the sources may

is characteristic for describing all levels and each component in a given level.

be at a certain stage of changes, as a development of the approaches from [1–6, 11].

Every phase of a NES and every emergent phase are composed of (Figure 3):

) a set of syzygies is illustrated for the case of NES, as follows [7]:

conversion. This generator has the following characteristics:

**•** Entropy (Thermodynamic) (EnTh) as a measure of disorder.

chaotic behavior of structures of complex systems (SAC).

An illustration of these characteristics is shown in Figure 2.

**•** The basic part and the feedback for the structure *COFB <sup>k</sup>*,

**•** The layer of connection from one level to another *CLNLi*

**•** The layer of connection to the base level *CLMPj*

**•** The main layer of the structure *MLj* where *k* = 0, 1, 2, 3; *i* = 1, 2, 3, *si j* = 1,…9.

**•** Information Entropy (EnI) as a measure of the limits of knowledge itself.

**◦** It is destroyed when the process is irreversible

than for NES components altogether.

**Figure 3.** Layers and structure of the KP of K(i) type for the NES example [11]

It can be noted that a given structure of KP for a NES type system has a fractal characteristic.
