# Entropy and Statistical Complexity in Bioelectrical Signals: A Literature Review
## 3 Results
### Complexity-Entropy Plane  
Once the information quantifiers, entropy, and SCM are defined, they can be interconnected through a novel conceptual framework referred to as the complexity-entropy plane. Traditionally, entropy has been employed to understand and quantify the complexity of a system or physical process, serving as a primary metric. While entropy measures the uncertainty or inherent disorder within a system, SCM, in turn, reflects the degree of order or disorder from the perspective of the system's organization and structure. Initially, in the 1990s, it was referred to as the complexity curve [56]. Later, in 2007, [PERSON] and his collaborators further advanced this graphical representation [23; 71], naming it the Complexity-Entropy Causality Plane (CECP) [23; 38; 42; 47; 69; 71]. It has also been recognized by alternative names, such as the Complexity-Entropy Plane (CE) [47; 48; 70], the H-C Plane [1], and the Entropy-Complexity Plane (EC) [57; 67]. Since its inception, the plane has been extensively applied across various scientific disciplines [23] and requires minimal preprocessing of the original signals [38]. The entropy-complexity plane refers to the region in the (H, C) space bounded by two limiting curves [57]. It is considered a tool [1; 23; 47; 69] and a conceptually simple yet remarkable methodology [16] for graphical representation [70]; a straightforward and efficient or parsimonious representation space [38]; a diagram [56; 67] or a set representing all possible (H, C) values [48]. It is employed for various purposes, such as analyzing and characterizing [47; 70], describing [69], evaluating [23], studying [67], and verifying [56]. For this purpose, it requires two essential measures, statistical complexity and normalized [42; 70] entropy [38; 42; 56; 69; 70]. Additionally, it incorporates distance and disequilibrium [69] to distinguish between [23] the possible states of a system [60] concerning its nonlinear dynamics and characteristics [12; 67]. Thus, a diagram showing C as a function of time it is useful for studying the temporal evolution of complexity. However, according to the second law of thermodynamics, the entropy of isolated systems increases monotonically over time, i.e., \(\mathrm{dH}/\mathrm{dt}\geq 0\)[8; 55; 57; 59; 67]. This indicates that the entropy H can be understood as a temporal direction [8; 67] or temporal dimension [38; 57]. The analysis of C in relation to H provides an alternative approach to studying the temporal evolution of SCM [38; 55; 57; 67]. In this context, entropy serves as a normalized temporal axis [67], represented on the horizontal axis with values ranging from 0 to 1 [57; 70], while the vertical axis is used to represent complexity [70]. Finally, to transition from C vs. H diagrams to C vs. t diagrams, it is necessary to adjust the entropy axis according to its temporal progression, either through expansion or reduction. It is important to note that, in general, the relationship between H and t is not typically straightforward [55]. Numerous practical applications have confirmed its effectiveness. These include its use in analyzing the inherent complexity of [23] dynamic [23; 42; 67; 69] systems [23; 70]; visualizing and studying the characteristics and changes in the dynamics of a complex [42] system [42; 67; 69]; characterizing and differentiating various types of noise [12], such as fractional Gaussian noise and white [48] noise [12; 23]; and distinguishing fractional Brownian motion [12]. Additionally, it is used to distinguish the chaotic [1; 12; 23; 47; 60], ordered [60], deterministic [1; 12; 23; 47; 48], and stochastic [1] nature of arbitrary [48] time series [1; 38; 47; 67], facilitating the differentiation between statistical uncertainty and algorithmic complexity [12]. Finally, it is employed to confirm anticipated qualitative behaviors [56].