# Entropy and Statistical Complexity in Bioelectrical Signals: A Literature Review
## 3 Results
### Statistical Complexity
This measure encompasses not only disorder but also the degree of correlation among structures within a time series [1; 16], a process, or a physical system under study [59; 67], as well as among successive elements of a sequence, focusing on their interaction and dependence [25]. The SCM is not only a method for measuring or quantifying the relationship between order and disorder but also a tool for capturing the regularity and randomness in the behavior of a physical system or process [5]. It presents two opposing extremes: disorder, exemplified by an ideal gas representing maximum randomness, and complete order, as in a perfect crystal. Both extremes exhibit zero or null complexity, lacking any relevant [6; 8; 23; 60; 61] or complex [67]. This is because, in these cases, the system's structure is entirely simple--either due to the total absence of patterns [16; 58] or the presence of perfect order [1; 58]. Additionally, SCM should exhibit predictable asymptotic characteristics and properties, vanishing in the idealization of a perfect crystal or an ideal gas [56]. It is also expected that the complexity measure reaches maximum values between these two extremes [58]. In contrast, its value is not zero for all other particle systems [56]; in other words, entropy and complexity are not null in an intermediate chaotic state [60]. Between these two particular extremes lies a wide range of values or an extensive variety of possible structures or physical levels within a dynamical system [1; 8; 61]. These levels should, first, be captured by the characteristics of the underlying probability distribution [8; 61]. Thus, the physical laws at each level of observation exhibit different values for imbalance, given that at each level, a new set of accessible states with their corresponding probability distribution is observed [56]. In this context, the evaluation of SCM provides additional insight or new information about the details and peculiarities of this distribution, which are not distinguished by conventional randomness measures [59; 61; 67]. Secondly, these levels should be measured comparatively, similar to how [PERSON]'s information theory captures randomness [8]. This measure must rely on a statistical description of the system at a given level [5; 56; 59]. For this purpose, the statistical complexity measure is often identified as a suitable theoretical framework [8; 67]. Moreover, the SCM can be evaluated using different entropy measures [63]. These two quantities--entropy and complexity--consider the system's probability distribution P [5] and compare it to a uniform distribution [47]. SCM uses P to extract the probabilities of each possible value of the variable and estimates a numerical value representing the complexity of the observed system [6]. Additionally, it incorporates the dynamics of the observed process, examining how it evolves over time [5]. It is essential to emphasize that complexity cannot be expressed simply as a direct function of entropy [57; 61; 67]. This means it cannot be directly derived from the entropy value provided by the system [67], as it involves a comparison between two probability distributions: that of the system and a uniform distribution [1; 67]. Multiple distributions may achieve the same entropy value; however, they differ in their corresponding complexity values. Furthermore, due to the scale of observation and the nature of its description, complexity cannot be measured uniquely [56]. Specifically, for an isolated system evolving over time, SCM values cannot be arbitrary [8; 55], as they must remain within a specific range, bounded by a minimum value \(\mathrm{C}_{\mathrm{min}}\) and a maximum value \(\mathrm{C}_{\mathrm{max}}\)[1; 8; 55; 57; 59; 67]. These bounds are determined by the dimensionality of the probability space and the functional form of the adopted disequilibrium [1]. Within this context, there exists a range of complexities between these bounds [59; 61; 67], which are, in turn, constrained by normalization criteria [55].