# Entropy and Statistical Complexity in Bioelectrical Signals: A Literature Review
## 3 Results
### Statistical Complexity  
Today, the Statistical Complexity Measure (SCM) [15], also referred to as structural complexity [67], is recognized as a fundamental concept in the study of complex systems. It characterizes the relationship between the system, its contained information, and disequilibrium on a specific scale [15; 23; 56; 59]. However, a significant contribution to the definition of complexity came from [PERSON] in 1986. He asserted that \"a complexity theorist, faced with the problem of describing an ideal gas, could not even use basic notions such as temperature or pressure. Therefore, our first requirement for physically useful complexity measures is that they must be probabilistic\" [68] (p. 908). In this context, the complexity of a dynamical system and the generation of patterns are represented by a mixture of structure and chaos [59]. Similarly, since the mid-1990s, statistical complexity based on the idea of disequilibrium was proposed by [PERSON], [PERSON], and [PERSON] [56; 61], commonly known as LMC [55; 58; 61]. This concept laid the foundation for further advancements in complexity measures. The LMC measure is characterized by its straightforward calculation and is grounded in principles commonly used in statistical mechanics [61]. It is expressed as C = D\(\times\)H [55] or C = Q\(\times\)H [61], where H represents the system's logarithmic entropy [58], and Q or D denotes the disequilibrium [55; 61]. Disequilibrium D is typically defined as the product of a normalization constant and an appropriate distance measure [8; 61], commonly the Euclidean norm [61] or the quadratic distance between two probability distributions--the equiprobable distribution and the system distribution [58]. The LMC measure is a function of probabilities [58], or of the discrete distribution, both of which imply that all its values are non-negative [55]. Furthermore, these definitions are based on the assumption of belonging or association with the accessible states N of a given physical system [55; 58]. Furthermore, statistical complexity measures can be viewed from three perspectives: (i) increasing with rising disorder or decreasing as order increases; (ii) being very small at high levels of either order or disorder, reaching a maximum value at an intermediate point; and (iii) increasing with higher levels of organization and decreasing as disorder or lack of order intensifies [8; 61]. In light of the above, the definition of statistical complexity should not be confined solely to terms of disorder [8; 56; 59]. Currently, statistical complexity incorporates foundational elements that have been developed over recent decades. Today, it is defined as the ability to quantify critical details of the underlying dynamic processes within a system [7]. Additionally, it is used to assess the dynamics of these processes, providing a measure of organization that is crucial for understanding both the amount of information and the structure contained within the dataset [63]. On the other hand, the SCM positions itself as a tool [23] or an indicator of hidden order [56; 59]. It is used to examine dynamical systems, differentiating between chaotic behavior and noise [23]. Additionally, it serves to describe systems with simple structures but complex dynamic properties, uncovering patterns [8; 23; 59; 61; 69], or intricate hidden structures [8; 59; 61] within their characteristics [23]. This highlights the paradox of complicated dynamics arising from basic structures [8; 23; 59; 61]. Furthermore, SCM is employed to characterize or uncover the complexity of time series [1; 16; 47; 57] or chaotic time series [67]. For the former, it offers a method to quantify the emergent structures within the system as it moves toward equilibrium [47; 57], while for the latter, it captures organizational properties that are not evident through conventional randomness measures [67].