# Entropy and Statistical Complexity in Bioelectrical Signals: A Literature Review
## 3 Results
### Complexity  
The literature presents multiple definitions of complexity across various fields [55; 56; 57], including economics, sociology, linguistics, biology, and physics, among others [58]. However, there is no consensus or universally precise definition of complexity [58; 59], particularly in physics [59]. Consequently, significant efforts have been devoted to defining it rigorously. The primary challenge in reaching an agreement seems to stem from the lack of a shared language among different scientific disciplines [58]. Additionally, various perspectives have emerged regarding its quantitative characterization, accompanied by numerous complexity measures and methodologies for analysis [59], which can be categorized based on the methods used for their computation [55]. For instance, some academics have first indicated that in computational sciences [56], concepts such as logical depth, algorithmic complexity [55; 56; 58], and e-machine complexity [55] are prevalent. Additionally, Lempel-Ziv complexity, [PERSON]'s effective complexity measure, and complexities of formal grammars are also considered [56]. While these complexity measures have demonstrated their effectiveness, they have the drawback of being extremely challenging to compute [55]. Second, in the field of natural sciences, complexity is employed to differentiate physical processes and address the challenges that arise when attempting to quantify it accurately [57]. Specifically, in physics, concepts such as the edge of chaos, self-organized criticality [58], and thermodynamic depth [55; 56] are explored. To illustrate complexity from the perspective of physics, its analysis is proposed using the ideal crystal and the isolated ideal gas as basic models or systems characterized by theoretically zero complexity [56]. The first system, the perfect crystal, exhibits total order, while the second system, the ideal gas, is characterized by complete disorder [56; 60]. In an ideal crystal, the available states are concentrated in a principal state with perfect symmetry. In contrast, in an ideal gas, the system can occupy any of its accessible states. Given this, it is important to emphasize that the information stored in the first system can be considered minimal, while in the second system, by construction, is maximal [56]. After analyzing these extreme cases, it is concluded that they are clearly non-complex [8; 59; 61]. Third, from the perspective of Information Theory, measures such as information and entropy are used to quantify the complexity of systems or processes [58]. These include simple complexity measures, effective complexity, and the K-S metric entropy rate [55]. Fourthly, complexity can also be calculated directly using the distribution function that characterizes the system, relying on approaches such as meta-statistics and the concept of disequilibrium, the latter known, for instance, as LMC. Metrics based on these principles enable straightforward calculations and natural evaluations grounded in statistical mechanics [55]. Furthermore, the literature has highlighted that various techniques are employed to evaluate complexity in physical systems, including data compression algorithms, recurrence plots, optimal predictability, symbolic analysis, and wavelet analysis, among others. These complexity measures capture diverse aspects of complex systems [59], proving particularly beneficial in the description of symbolic dynamical maps as well as in ideal free-fermion systems out of equilibrium [55]. On the other hand, in the realm of dynamical systems, complexity is often associated with systems exhibiting chaotic behavior, in contrast to periodic or stochastic systems. The characterization and distinction of these systems, as well as the differentiation of purely random behaviors, have been longstanding areas of study [47]. Specifically, the complexity of a time series is characterized by the heterogeneous structure of the data and the variability of the series over time [62; 63; 64].