# Entropy and Statistical Complexity in Bioelectrical Signals: A Literature Review
## 3 Results
### Statistical Complexity
The quantification or measurement of SCM, from a mathematical perspective [8], is expressed as the product of the system's disequilibrium Q [1; 8; 55; 56; 70] and the entropic information quantifiers [8; 55; 70; 57] or an information measure [1]. This disequilibrium Q can be determined by comparing the distribution of the signal in question, P, which represents the functionality of the observed process, with a uniform or maximum entropy probability distribution, P\({}_{\text{e}}\)[8; 56]. It is not possible to directly link the concept of disequilibrium within a system to the idea of complexity [56]. Disequilibrium is viewed as a distance D [8; 17; 56; 59; 60; 61], in a probabilistic space [61], represented by Q [8; 59; 61], which reveals the system's architecture [8; 59] or the probabilistic hierarchy [15; 56]. This is achieved by reflecting the difference or proximity between the system's probability distribution P and the uniform distribution P\({}_{\text{e}}\)[8; 17; 56; 59; 60; 61], the latter representing an equilibrium state [59], in the context of Gibbs' statistical mechanics [61]. SCM possesses a global character, as its value remains constant under different orderings of P [16]. This distance reaches its maximum when a single component of P equals one and all others are zero [59], suggesting the existence of more probable states among those available [8; 15; 56; 59]. For instance, a unique pattern arises from a strictly increasing or decreasing series, where no other classes of patterns exist. In this case, complexity is null, as entropy is zero and the distance to the uniform distribution is maximal. In contrast, for white noise, the distance to the equilibrium distribution is zero, as its entropy is maximal [48]. This interpretation of disequilibrium distinguishes systems such as the crystal, which exhibits high disequilibrium due to a dominant state, and the ideal gas, which has minimal disequilibrium because of its uniform distribution. Additionally, two conditions are established for disequilibrium: (i) it must be greater than zero to positively measure complexity and (ii) it must be equal to zero in the limit of equal probability [56]. The metrics and the induced distance D, key elements in defining Q, provide various options [59]. To estimate disequilibrium Q: (i) the Euclidean distance between two points in space is often used; however, this measure overlooks the probabilistic nature of P, ignoring the stochasticity of the vectors [8; 61]. (ii) The Wootters distance is employed, which measures the difference between two distributions with the same number of values in their discrete variables [8]. [PERSON] posits that statistical errors cause observed frequencies to slightly differ from the true probabilities. This statistical distance quantifies not only these differences but also how far the probability states deviate from the ideal frequencies. Consequently, two initial states are indistinguishable if the difference between the true probabilities is smaller than a typical fluctuation or random variation from the expected value [8; 61]. (iii) Disequilibrium Q can also be estimated using two classes of divergences: divergences defined as relative entropies, including associations like [PERSON] with Shannon, Tsallis, and Renyi; or divergences derived from entropic differences, including associations like [PERSON] with Shannon, Tsallis, and Renyi [8].