# Entropy and Statistical Complexity in Bioelectrical Signals: A Literature Review
## 3 Results
### Complexity-Entropy Plane
It is important to clarify that, in the analysis of stochastic time series, these exhibit high entropy and intermediate complexity, interestingly positioning them near the lower-right corner of the complexity-entropy plane. In contrast, chaotic time series, such as the Henon, Logistic, Skew, and Schuster maps with \(z=3/2\), are characterized by high complexity and low entropy, situated around the maximum complexity value on the plane [6; 71]. Furthermore, it has been demonstrated that the plane can identify both slow and rapid changes in the state of mechanical components [38]. An additional dimension for observing system dynamics is provided by the plane [15; 70], which also incorporates the dynamics of physiological states [15]. The study of diseaseshas shown promising efficiency in detecting pathologies [16; 70] and mental states, which are better appreciated and understood through this representation. Furthermore, it is used to evaluate a variety of conditions, including aging [70]. Similarly, it enables clear separation and distinction between data originating from diverse groups, sources, or conditions [15; 47; 52]. For example, the plane has been applied in the clinical field for analyzing patient-specific signals in individuals with various cardiac conditions [16]. Other studies, using the plane as a reference, have explored rhythmic brain dynamics and their relationship with mental states. It is suggested that these states emerge from the dynamic interaction between physical and functional levels, generating patterns of oscillatory brain activity. These patterns are observed in various oscillatory bands--delta, theta, alpha, beta, and gamma--and play a key role in information processing within the brain. Specifically, the posterior-parietal and occipital lobes exhibit regions with higher entropy and complexity in the alpha band, suggesting that these areas are involved in more diverse and complex information processing [1]. The plane also enables efficient deterministic and statistical analyses [16], with the latter being particularly useful in the study of biological systems [70]. Finally, there is substantial evidence suggesting that diseases and the aging process [65; 70] are, first, associated with a decline in complexity [70], and second, with a reduction in an individual's adaptability, thereby decreasing the information provided by output variables [65]. However, despite the well-defined boundaries of the C-H plane or diagram, the comprehensive analysis of its intrinsic topology remains unresolved. In particular, the joint distribution of data points from common time series within the plane is not yet fully understood. This distribution would be valuable for developing test statistics [48]. Additionally, several challenges associated with the plane have been identified. First, the complexity-entropy curve of generalized fractional-order at a single scale does not provide sufficient features to identify the system. Second, the implementation of entropy algorithms does not account for dynamic complexity. Third, the high computational cost of certain entropy measures poses a significant challenge. Fourth, the structural complexity of transformations between sequential patterns adds further difficulty [49]. In light of the above, the present research proposal considers the use of entropy-complexity analysis to detect functional dyspepsia (FD) through electrogastrography. By analyzing the appropriate bioelectrical signals associated with FD, entropy-complexity measures can be obtained, providing valuable information about the organization and complexity of the activity in patients with FD.