# Entropy and Statistical Complexity in Bioelectrical Signals: A Literature Review
## 3 Results
### Entropy  
The concept of entropy emerged in the 19 th century [9], introduced by the German physicist [PERSON], who used it to describe the chaos in energy distribution, indicating the degree of disorder in a system [10]. As a physical quantity, it depends on the system's parameters, is independent of the process performed, and is proportional to the system's size [5]. This concept was later developed by [PERSON] and [PERSON], who applied it to model molecular disorders [11]. Entropy has its origins in the fields of statistical physics, quantum physics, and thermodynamics [12], and its quantification is based on probability [13]. In the field of thermodynamics, entropy was introduced to describe the probability distribution of molecules in gaseous or liquid systems [14] and to quantify the degree of disorder or randomness inherent in a physical system [5]. Similarly, in the field of statistical mechanics, entropy represents a measure of uncertainty or disorder within a system [5]. Later, in 1948, the concept of entropy was adapted for use in information theory and signal analysis [9]. Entropy is related to concepts such as information, system order, and energy [15]. For instance, in the context of energy distribution, it is established that the more chaotically energy is distributed, the higher the entropy [10]. Entropy is a fundamental concept with multiple interpretations derived from various scientific and technological fields. According to some authors, entropy is defined as a basic quantity with specific interpretations, associated with disorder, the volume of state space, and the lack of information [16] (p. 39). Entropy represents a value that indicates the level of randomness in a signal, as well as the amount of information required to predict the behavior of the data without prior knowledge [17]. Additionally, it is proposed that entropy allows for the evaluation of randomness and the predictability of systems [18], or the absence of order and the inability to predict them [19]. Although there is no universal agreement on the definitions and quantification of entropy [15], it is broadly defined as a statistical measure widely used to describe and quantify certain attributes, such as irregularity [9; 20; 21; 22; 23; 24], complexity [9; 22], uncertainty [20; 21; 23; 24], and unpredictability [9; 25] of a signal [9; 22; 26], system [21; 22; 23; 25], or time series [24]. It also quantifies the lack of order, which is determined based on an associated probability measure [21; 25]. Entropy constitutes a quantitative measure that represents the level of disorder or uncertainty [10; 12; 15] inherent in a given system [15; 10]. In time series, entropy indicates the level of disorganization in the configuration of observed sequential patterns [25]. It is also defined as a fundamental tool for measuring system complexity, where more complex systems typically exhibit higher levels of entropy [10]. Entropy rate estimators are often used to measure the complexity of a signal, based on the premise that system complexity increases with the amount of uncertainty or information the signal produces with each new sample [27]. Likewise, it is one of the most widely used methods for analyzing and measuring the complexity of time series [28]. Moreover, entropy has been defined as a measure of the amount of information [9; 29] contained in a signal [9] or system with respect to the total number of possible states [1]. It precisely quantifies the unexpected data present in the system or signal [9] and is widely used in the field of signal analysis [30], nonlinear time series, and dynamical systems [29]. Additionally, entropy is defined as a measure of the probability of the next state of a system based on the current known state [31]. It is important to highlight that entropy considers the probability of observing a specific state in a system without accounting for the significance of any particular state [14].