# Entropy and Statistical Complexity in Bioelectrical Signals: A Literature Review
## 3 Results
### Entropy
This measure is also interpreted as the loss of information in a time series, quantifying the probability of the system's next state based on its current state [13]. Similarly, it is understood as the rate at which new information is generated, indicating the likelihood of producing additional patterns in the signal and reflecting its complexity. As the probability of generating a new pattern increases, the complexity of the signal rises [32]. Additionally, it is used to measure the likelihood of repeating similar patterns within a signal, which indicates the regularity of the time series [33]. Entropy is closely related to the probability of events in a system. When the probability of events is high, the information obtained from subsequent states is low, resulting in lower entropy values. This indicates greater regularity in the system [31], whereas a high entropy value suggests randomness in the time series [33]. Conversely, when the probability is low, subsequent states provide more new information, increasing entropy and suggesting greater irregularity or complexity in the pattern [31]. In other words, higher entropy values indicate lower probability and a greater amount of new information generated by future data points in the time series [13]. In this sense, it can also be considered that the amount of entropy present in an observed signal indicates that high entropy corresponds to scenarios where all possible outcomes are equally probable and highly uncertain. Conversely, low entropy in a signal occurs when some outcomes are more likely than others, thereby reducing uncertainty [5]. Additionally, a signal or time series with a low entropy value is more deterministic, making it more likely to follow a specific pattern. On the other hand, a signal with a high entropy value is less deterministic, meaning it is more likely to be random and unpredictable [26]. The normalization of this measure within a range of 0 to 1 is crucial, with 0 indicating an ordered system and 1 denoting a random, uncorrelated system. This normalization facilitates the evaluation of the complexity or inherent randomness of the system [1]. If the entropy S(P) is 0, all possible events with probability \(\mathrm{p_{i}}\) will occur, reflecting a completely predictable system [23]. In other words, when entropy approaches 0, the system is highly probable and provides little new information about subsequent states [13]. Thus, the two extreme situations--complete knowledge (perfect order) and total ignorance (absolute randomness)--can be considered trivial cases. For a given probability distribution P and its associated information measure I(P), a quantity of disorder H is defined. This quantity of disorder is the ratio between the information measure I(P) and the maximum information measure I\({}_{\mathrm{max}}\) or I(P\({}_{\mathrm{e}}\)), which corresponds to the uniform distribution. Therefore, H is bounded between 0 and 1 [8]. Finally, the maximum possible value of entropy depends on the information measure used to describe the system under consideration. Finally, a formal definition of entropy for a discrete random variable, mathematically calculated from its probability mass function, is \(\mathrm{p_{x}}(x)=\mathrm{Pr}(X=x)\) where \(x\) belongs to the state set \(\Omega\)[12]. Its definition is based on the three fundamental axioms known as the Shannon-Khinchin axioms. These axioms state that entropy is invariant under the permutation of probabilities, increases with the greater dimensionality of the state space, and possesses a recursive property that demonstrates the reduction in entropy when merging states [12]. Information Quantifiers: Entropies  
The aforementioned thematic focuses addressed the first two steps for discretely processing continuous signals: (i) through sampling and (ii) the probability distribution P. Thisthematic focus develops the third stage: quantification.