# Entropy and Statistical Complexity in Bioelectrical Signals: A Literature Review
## 5 Conclusions  
Continuous signals can be effectively discretized through sampling and probability distribution. Sampling enables measurements to be taken at regular intervals, while the probability distribution (P) provides insight into the uncertainty and variability of physical systems. Determining P using methods such as histograms, symbolic dynamics, Fourier transform, or Wavelet transform, among others, is essential for calculating entropy, a key measure in information theory and thermodynamics. Entropy measures disorder and uncertainty in physical systems. In Information Theory, it is used to quantify randomness in signals and time series. Different forms of entropy, such as Approximate Entropy (ApEn), Sample Entropy (SampEn), and Permutation Entropy (PE), have specific applications and limitations for analyzing biological data and signals, reflecting the complexity and regularity of systems. In the medical field, entropy measures have been used to analyze bioelectrical signals in neurodegenerative diseases and, to a lesser extent, digestive disorders. Additionally, techniques such as Permutation Entropy, Fuzzy Entropy, and Multiscale Entropy have specific applications in the study of diseases and physiological signals. The entropies FuzzyEn, ApEn, SampEn, PE, and MSE share key characteristics that make them useful for time series analysis in various contexts. FuzzyEn stands out for its robustness and accuracy when analyzing small and short datasets, while ApEn and SampEn exhibit resistance to noise, making them suitable for both deterministic and stochastic processes. PE, on the other hand, is effective in measuring complexity in sequences and time series, particularly in neuronal and nonlinear scenarios, and it adapts well to different types of real-world data. Finally, MSE stands out as a versatile tool for analyzing complexity and irregularity in physiological signals and dynamic systems, especially under noisy conditions and across multiple temporal scales. These characteristics highlight the potential and capability of these entropy measures to address complex problems in biomedical data analysis. Additionally, ApEn, MSE, SampEn, and PE share common limitations that affect their performance in time series analysis. MSE faces issues with accuracy in short recordings and discrepancies across scales, making it challenging to compare complexity between series. PE, while effective in certain contexts, is limited to the order of values, ignoring dynamic or amplitude differences, which reduces its ability to capture complete patterns in finite datasets. SampEn, on the other hand, is inefficient for long or erratic series, and its accuracy depends on carefully selected parameters, complicating its use for real-time analysis. Finally, ApEn is known to be biased, especially with short signals, and its sensitivity to data length and parameter selection diminishes its consistency compared to other measures. These limitations hinder more robust analysis under real-world conditions. Finally, the complexity-entropy plane combines entropy and complexity to provide an integrated perspective of systems. This approach allows for the study of system dynamics, the characterization of noise, and the differentiation between types of time series. While effective in the analysis of diseases and aging, it faces challenges in implementation and precision. Its limited application, for instance, in the analysis of digestive disorders through electrogastrography, highlights the pressing need to combine these concepts to enhance clinical understanding and diagnosis. Additionally, it underscores a knowledge gap concerning the use of ITQ. **Author Contributions:** Conceptualization, L.G.G.A. ; methodology, L.G.G.A. ; validation, L.G.G.A. and M.C.P. ; formal analysis, L.G.G.A. ; investigation, L.G.G.A. ; resources, L.G.G.A. ; writing--original draft preparation, L.G.G.A. ; writing--review and editing, L.G.G.A. ; visualization, L.G.G.A. ; supervision, M.C.P. ; project administration, M.C.P. ; funding acquisition, M.C.P.