# Information, Thermodynamics and Life: A Narrative Review
## 1 Introduction
### [PERSON]'s Information  
Information is probably one of the most complex scientific aspects. In 1948 [PERSON] published a study entitled \"_A Mathematical Theory of Communication_\" [11], which focused on the various ways of information encoding from a transmitter to a receiver. The main idea of this seminal work was to link information with probability. In this fundamental work, [PERSON] mainly used the concept of probability theory in information. If \(Z^{L}\) is the set of all \"words\" of a length \(L\) for a finite alphabet \(Z\), then each \"word\" \(w\) is a possible message sent by an information source, and consists of a \"stationary stochastic process\" [12]. Thus, if \(P(w)\) is defined as the probability for a word \(w\) to be sent as a message the information it contains under [PERSON]'s information definition is:  
\[I(w):=-\log_{2}P(w) \tag{1}\]  
Figure 1: Diagrammatical representation of information theory. In that sense [PERSON] introduced the term of \"informational source\" as a pair (\(X\),\(p\)), where \(X\) is a finite set of objects and \(p\) is the probability function assigning to every \(x\in X\) the probability \(p(x)\) of occurrence. This approach had as a consequence the definition of the average quantity of an information source (\(X\),\(p\)), which is defined as:  
\[H(X,p)=-\sum_{x\in X}p(x)\log p(x) \tag{2}\]  
The \(H\)(\(X\),\(p\)) function is also called the entropy function, where the total entropy can be described:  
\[H_{j}=\sum_{i=0}^{n}H_{j,i} \tag{3}\]  
The first applications of his theory included the computation of Channel Capacity with the induction of information to _bits_, which is the abbreviation for \"_binary digit_\" [9]. Bits can exist in two states, which can be abstractly represented by the digits 0 and 1. In that sense every information can be described as the combination of binaries. Further on, bits can be used to implement information by means of a semiconductor, magnets, condensers and so on. In general, information can be divided in three main processes: (a) Storage, (b) Transmittance and (c) Processing [10,11]. Moreover, information should have a content, some sort of meaning that will make sense to the receiver (semantics) [13] and finally, a critical aspect of information theory is the transmission. This includes several discrete stages, which are: (a) the message, which includes the information per se, (b) the transmitter, (c) the encoder, which transforms the information into bits, (d) the channel of information transmittance, (e) the decoder, which decodes the digital information, (f) the receiver (also called the destination) and (g) the noise source, which is beyond the control of the transmittance process and interfered with the information (Table 1). The most basic concept of classical information theory is that of Shannon entropy [11,13]. This quantity is related to the information load of measuring the value of a random variable \(X\). In a sense, entropy measures the uncertainty we have about predicting the value of \(X\) before observation. Thus, in the literature entropy is also referred to as an uncertainty measure. The importance of entropy as an information load is fundamental to applications because its value determines the minimum amount of information we need to retain from a message in order to be able to reproduce the original information. This result is included in [PERSON]'s Noiseless Coding Theorem [14,15], which is fundamental to information theory. Essentially, the concept of entropy comes to answer the basic question that has to do with how much natural resources we need to consume in order to manage some information.