# Entropy and Statistical Complexity in Bioelectrical Signals: A Literature Review
## 1 Introduction  
In the field of biomedical engineering, Information Theory Quantifiers (ITQs) [1] have been used to study neurodegenerative, cerebrovascular, and cardiovascular diseases and, to a lesser extent, gastric disorders. These methods, based on complexity and entropy, have allowed the analysis of time series to capture the variability in bioelectric signals, facilitating early detection and evaluation of their progression, which represents a promising advance in medical diagnosis and care based on data.  
The purpose of this review article is to present the findings of the theoretical meta-analysis on the use of ITQ in biomedical engineering, based on the review, explanation, and analysis of academic literature related to nonlinear analysis methods, statistical complexity, and the complexity-entropy plane. All of these aim to highlight the knowledge gap regarding various perspectives and existing theories in this field.  
The study seeks to provide a solid theoretical framework, with the intention of serving as an international reference. Furthermore, it aims to contribute to medical knowledge through the field of engineering, by providing multiple perspectives that reinforce existing theories in the current context. The application of ITQ concepts in medicine not only enriches the academic landscape but also opens new opportunities for analysis in this field.  
The descriptive hypothesis guiding this review article posits that a comprehensive meta-analysis of existing perspectives and theories will enable the identification of knowledge gaps, as well as innovative approaches that contribute to advancing the study in this field. To facilitate understanding of the document, it is important to note that the abbreviations used throughout the text are clearly defined in Appendix A.  
This review article presents previous research on statistical complexity and its medical impact, which includes a search of relevant scientific literature on topics such as probability distribution functions and entropy, using databases such as Web of Science and Google Scholar. Seventy sources were identified, including articles in academic journals and other documents, mostly from Europe and America, distributed over the last five years and earlier periods to ensure a comprehensive overview. Documents were classified using the Latent Dirichlet Allocation (LDA) model to extract key themes for subsequent analysis and interpretation of the themes and relationships between the studied variables. The findings highlight advances and gaps in the field to justify and guide future research.  
It was concluded that continuous signals can be discretely analyzed through sampling, probability distributions, and quantization, the latter being essential to calculate entropy. Entropy measures disorder and uncertainty in physical systems, and its application in information theory allows us to analyze signals and time series. Various entropy measures, such as Fuzzy Entropy, Approximate Entropy, Sample Entropy, Permutation Entropy, and Multiscale Entropy, among others, offer different approaches to evaluating complexity and regularity in biological data and signals. Each method has its advantages and limitations, making it necessary to select the appropriate one according to the context and nature of the data.  
From a clinical perspective, entropy measures have demonstrated significant potential in the early detection and monitoring of various pathological conditions. The complexity-entropy plane graphically represents the relationship between disorder and structure in a system. This approach is useful for studying dynamics, characterizing noise, and distinguishing between types of time series and has proven effective in the analysis of diseases and aging. Thus, entropy measures not only enhance the theoretical understanding of biological systems but also provide practical tools to improve pathology detection in clinical contexts.