This first part of the book focuses on the main theoretical concepts that are the necessary raw material to construct the theory of cyber‐physical systems to be proposed in the second part of the book. In this chapter, we begin this journey with the concept of system. The idea is to review the different meanings of the word, starting from the dictionary definition and moving toward a more technical one, which is used in the discipline of Systems Engineering. From there, a general method to organically demarcate the boundaries of a particular functioning system and everything else (i.e. its environment) will be proposed. We will further postulate the conditions of the existence of that particular functioning system as such. These conditions are divided into three levels that articulate the relation between that particular system and its environment. Different ways to classify systems will also be presented followed by an initial analysis of Maxwell's demon – a well‐known thought experiment that was proposed to challenge the second law of thermodynamics. With this chapter, we aim to clarify the relation between the scientific domain whose object is a functioning system in general and its possible particular material realizations. In this sense, we argue that this theoretical methodology is essential not only to scientifically understand systems in general but also to engineer new or rectify particular existing systems.

2.1 Introduction

Let me start by showing a dialogue I had with my 5‐year‐old daughter:

• What is a car?
• It is a system designed to take people from one place to another, in a faster way and with less effort than walking.
• What is a system?
• Well (…), in this case, it is a machine composed of things working together to perform some action.
• And, in the other cases?

My goal in this brief section is to provide satisfactory answers to these two questions in italics. The first step is to check which are the definitions of “system” that the dictionary gives.

It is clear the meaning I used to answer to my daughter is (1). At this point, two remarks are needed. First, not everything that is a regularly interacting or interdependent group of items forming a unified whole constitutes a system. For example, a clock, a car, or a computer are usually considered systems, while open markets or football teams are not (even though they might). This relatively arbitrary daily usage of the word shall be abandoned later in this chapter. The second remark is that the different meanings of the same word may create a series of confusion. While the meaning (1) mostly refers to the concrete reality, (2) and (3) seem to refer to symbolic domains, (4) and (5) are fuzzier and more subjective. Since this book is about engineering, (1) is the most appropriate meaning as our starting point.

With those warnings given, we are almost ready to transform the word “system” – our first raw material – into a concept that will become operational in the proposed theory of cyber‐physical systems. Before we begin, though, it is important to describe how we will proceed. The first move is to provide a descriptive technical definition of what a system is following the well‐established discipline Systems Engineering [2]. After this presentation, we can finally specify how it is possible to demarcate and articulate a particular functioning system with respect to its environment.

2.2 Systems Engineering

This section revisits the pedagogical exposition of the main technical terminology employed in Systems Engineering following the textbook Systems Engineering and Analysis [2]. The definition below states its answer to the question what is a system?

This definition is constructed upon four concepts:

1. Components: the elementary material parts – the building blocks – of the system.
2. Attributes: the properties of the components, or of the system as a whole.
3. Relations: the connections between components.
4. Function(s): what the system needs to accomplish.

It is quite straightforward to think in these terms. There are some specific pieces that are combined to form a whole that, if put together in such an organized form, can perform a predetermined task. Think about the do‐it‐yourself trend of building furniture, or even a house.

It is also important to point out that systems are always (directly or indirectly) related to dynamical processes. In other words, systems change. These changes usually refer to the state (situation) of the system at a specific point in time and in space. A series of changes in its state is called behavior. A process then refers to a sequence of behaviors. The function of the system is the outcome of a process or a series of processes.

It should be clear that the function of a particular system cannot be performed by any of its individual components alone, reminding us that the system is more than the sum of its parts. Roughly speaking, each component has its own role based on its attributes and interrelations. Depending on the role in the system, the different components can be classified into one of the following categories.

1. Structural components: The (quasi‐)static parts of the system.
2. Operating components: The parts that perform the processing.
3. Flow components: Whatever (e.g. material, data or energy) is processed by the systems.

Structural components usually provide the support for the operating components to process the flow components. Before entering the system, the flow components are called inputs; the flow components that leave the system after processing are called outputs. The process of transformation from inputs to outputs that is performed inside the system always requires a motive force, either internal or external to it. Note, though, that not all systems have such a transformation process as their main function; there are systems whose function is transportation (i.e. flow of materials or data), or structural support for other systems to work (i.e. a highway, a bridge, or a railway). Nonetheless, all functioning systems (actively or passively) do work in a physical sense, and thus, energy is always converted in, by, or through systems. Systems may also function in a hierarchy: components can be systems in their own right, but, with respect to another broader system, they are simply subsystems. There also exist subsystems composed of other subsystems, and such a regression may go on as needed.

The following example illustrates all that has been discussed so far in this chapter.

What is of utmost importance for analyzing and engineering a system is to demarcate its boundaries, limits, and scope considering its particular function(s) while articulating it with its external world, its environment. In this sense, the focus needs to be on functioning systems, or systems that have potential to function. This topic will be the focus of the next section.

2.3 Demarcation of Specific Systems

The definition of a particular system is usually arbitrary or assumed as given. When someone talks about a car, anyone listening should have a very clear idea about that system. But, this might be a trick: is a car without an engine, or wheels, still a car? Similar kinds of discussions are very common in other domains as well. For example: should an oat‐based drink be called oat milk?

In the legal domain, this definition is normative, usually as result of a deliberative process so that a definition can be imposed to indicate which is the correct word to name a given thing. The same happens with the word “car.” Each country has its own legal definition of what is considered a “car” indicating who is eligible to drive, or what taxes are to be paid. However, as we have discussed in the previous chapter, scientific concepts are different from words used in other practices: the former exist in a specific theoretical discourse whose meaning is completely defined by the formal structure of the theory they are part of. The scientific meaning of the word “car” then needs to be very well‐defined if it is to be considered a scientific concept. The question remains: how could such a theoretical concept be defined? The answer, once again, might be elusive: it depends on the scientific theory you are dealing with.

Since this chapter is about systems and how to scientifically define particular systems, our answer to that question will follow the solution we offer to the demarcation problem, where the system boundaries need to be defined with respect to everything else, which is referred to as environment. In other words, the problem is how to draw a line of demarcation between the system and the environment. This demarcation should not only indicate a functional relation but also a structural one. In this sense, the demarcation problem concerns both (i) how the system functions and (ii) how it is articulated with the environment so that its functioning can endure.

This definition indicates the theoretical challenges ahead of us. Two remarks are important: (i) the solution of the demarcation problem determines at the same time what is internal to a particular system, and what is not, and (ii) from the proposed demarcation, the articulations and interactions between that particular system and everything else need to the determined, which also determines its level of autonomy. Clearly, other systems are also part of the environment, as well as other instances of reality that affect and are affected by such a particular system under investigation. Looking at the broader picture without specifying any particular system, we see a whole that is constituted by several systems that are related to each other in different manner and degree. In this case, the whole is called complex while articulated in dominance so that some relations may subordinate the others, affecting the system at different levels and by different instances. The case of the smart meter and the smart/stupid grid presented in Chapter 1 illustrates this idea.

The following proposition solves the demarcation problem stated in Definition 2.3.

From this proposition, we can derive some interesting consequences. First, the system demarcation refers only to particular realizations of systems, not systems in general; on the other hand, this demarcation approach only makes sense if a theory of systems in general (as the one postulated here) exists. Second, a particular system whose PF is physically impossible cannot exist as such (e.g. a communication system designed to work outside Shannon's limit cannot exist); however, in some particular cases, it might exist as a thought experiment to challenge such an impossibility (this is the case of Maxwell's demon to be studied later in this chapter). Third, even if such a particular system is possible, it may not exist owing to conditions internal to its operation, and thus, the system cannot be established to perform its PF (e.g. a quantum personal computer is not yet possible because of operational instabilities related to quantum phenomena that the current technology cannot solve, or the lack of personnel capable of operating a given machine). Fourth, external events may also affect the system's conditions of reproduction (e.g. an earthquake that devastates the transportation system of a given city, or the lack of investment in education). Lastly, systems are not only affected by external events but also affect what is external to them (e.g. air pollution).

The starting point to demarcate a particular system is its technical description, i.e. its components that are combined to perform a given function. However, as we have discussed, these elements and their combinations are not enough to solve the demarcation problem following Definition 2.3: we have to describe what is needed for the system to function! To make this discussion less abstract, let us return to our “car” example.

As expected, PS, PF, and C1 are very well defined (although the list of the example above should be longer to be complete), while C2 and C3 could be as long as needed (but never exhaustive). The engineer or analyst task is to select C2 and C3 so that the most relevant instances and factors are included depending on the context they are dealing with.

Let us provide another example, now a new wind turbine that does not yet exist but is being designed.

As before, PS, PF, and C1 are very precise, while C2 and C3 are unbounded. In this case, this particular wind turbine does not materially exist, but it is still only a conceptual system. This nevertheless indicates the main determinations that a material realization of such a wind turbine are subjected to in order to function. The differences of material and conceptual systems will be discussed in the next section.

To conclude this section, we will present a proposition that posits the importance of the demarcation process.

It is also important to remember that the object of knowledge (the particular system that is subjected to the demarcation) is not the same as the material object (the real existing system), and they exist in different domains. However, the demarcation, as a theoretical process performed in the object of knowledge, produces a knowledge effect on the material object in the specific environment in which it exists or will potentially exist.

2.4 Classification of Systems

There are many ways in which systems can be classified according to their own characteristics or the focus of analysis. A proper classification is very important as it indicates the correct theoretical and experimental tools that are needed to develop objective knowledge of a particular system. In the following subsections, we will address a few general classes of systems, namely [2]: (i) natural and human‐made, (ii) material and conceptual, (iii) static and dynamic, and (iv) closed and open. Other classes of systems will be defined in the upcoming chapters as we introduce new concepts.

2.5 Maxwell's Demon as a System

This section deals with an interesting problem of thermodynamics, a field of physics defined as follows [8]: science of the relationship between heat, work, temperature, and energy. In broad terms, thermodynamics deals with the transfer of energy from one place to another and from one form to another. The key concept is that heat is a form of energy corresponding to a definite amount of mechanical work. Among its fundamental laws, the first and second ones will be introduced here in brief. The first is the law of conservation of energy, which states that the change in the internal energy of a system is equal to the difference between the heat added to it from its respective environment and the work done by the system on its respective environment. The second law of thermodynamics asserts that entropy (which, in very rough terms, quantifies the degree of organization) of isolated (closed) systems (i) can never decrease over time, (ii) is constant if, and only if, all processes are reversible, and (iii) spontaneously tends to its maximum value, which is the thermodynamic equilibrium.

Such fundamental laws of physics were postulated in the nineteenth century when the study of heat transfer and heat engines was widespread because of the needs of the industrial revolution. As discussed in the previous chapter, this is another example of how relatively autonomous scientific knowledge can emerge from technical needs determined by a specific socioeconomic conjuncture [9]. This relative autonomy of the theory allows scientists to pose interesting thought experiments. One of the most famous is Maxwell's demon, in which the second law of thermodynamics would hypothetically be violated [10]. This experiment is defined next.

Figure 2.1 depicts the situation. Our goal in this subsection is to analyze this problem as a system, indicating its (theoretical) conditions of existence and its PF. The idea here is not to solve this conundrum but rather analyze it as a system to properly define the problem and its characteristics. This should clear our path to theoretically work on the problem and then produce more knowledge about this object. Note that Maxwell's demon will also be studied in future chapters, and thus, it is worth for the reader to familiarize with it.

2.6 Summary

In this chapter, we went through different meanings of the word “system.” Among its different usages, we employed the definition and conceptualization from Systems Engineering as our theoretical raw material to then produce a scientific concept. From the general formalization of a system based on its components with their own specific attributes combined to perform a specific function or specific functions, we defined and solved the demarcation problem. The demarcation problem refers to how a particular system – determined by its peculiar function – is articulated with everything else by means of its conditions of existence. The demarcation is a theoretical process, exclusively symbolic, that produces objective knowledge of particular engineered objects that are conceptualized as functioning systems, which already exist or might exist. We also indicated different forms into which systems can be classified with respect to their own characteristics. Different examples were presented to illustrate the most important topics. At the end of this chapter, we dedicated a section to analyze as a system one classical thought experiment that will reappear in the following chapters: Maxwell's demon.

Exercises

1. 2.1 Residential heating system. There are different ways to heat a house during cold periods as indicated by the USA Energy Department [14]. The idea here is to apply the concepts learned in this chapter to analyze residential heating.
   1. Consider an electric heating system connected to the main grid (as any other appliance of your house). Demarcate this system following Example 2.3.
   2. Classify the system demarcated in (a) following the examples presented in Section 2.4.
   3. During the winter months, the electricity demand in households with electric heating grows as the temperature decreases. Think about a heating system that could function without electricity from the grid. Demarcate this potential heating system and compare it with (a).
2. 2.2 Boolean algebra and logic circuits. George Boole, an English mathematician and philosopher from the nineteenth century, proposed in his first book in 1847 a mathematical approach to logic by using mathematical symbols to represent classes of objects and then to manipulate them by mathematics [15]. In another groundbreaking work dating to 1938, Claude Shannon proposed in his Master's thesis a way to materially realize Boolean algebra by circuits [16]. They are represented by truth tables and logical circuits as illustrated in Figure 2.2.
   1. Analyze as a system (similar to Exercise 1) the logic gates AND, OR, and NOT, which are the basis of all logic circuits.

      

   2. Propose a way to materially realize these three logic gates based on (a).
   3. Follow the same steps used in (a) to analyze the proposal in (b), identifying the main differences between the conceptual system and its potential material realization.
   4. Read Shannon's Master's thesis [16] and discuss the importance of such a discovery.

   PS The reader is suggested to play with online Boolean algebra calculators (e.g. [17]) as an extra task; a starting point could be the calculation of the truth tables presented in Figure 2.2.

References

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