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.
Definition 2.4 Maxwell's demon [11] Maxwell's demon, hypothetical intelligent being (or a functionally equivalent device) capable of detecting and reacting to the motions of individual molecules. It was imagined by James Clerk Maxwell in 1871, to illustrate the possibility of violating the second law of thermodynamics. Essentially, this law states that heat does not naturally flow from a cool body to a warmer; work must be expended to make it do so. Maxwell envisioned two vessels containing gas at equal temperatures and joined by a small hole. The hole could be opened or closed at will by “a being” to allow individual molecules of gas to pass through. By passing only fast‐moving molecules from vessel A to vessel B and only slow‐moving ones from B to A, the demon would bring about an effective flow from A to B of molecular kinetic energy. This excess energy in B would be usable to perform work (e.g. by generating steam), and the system could be a working perpetual motion machine. By allowing all molecules to pass only from A to B, an even more readily useful difference in pressure would be created between the two vessels.
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.
Figure 2.1 Illustration of the Maxwell's demon thought experiment.
2.5.1 System Demarcation
The Maxwell's demon thought experiment can be analyzed as a hypothetical system. The idea here is to provoke the reader to think about this procedure and be critical about it. Different from the other examples, we are dealing with something that does not and cannot exist in the real world like a car or a wind turbine. On the other hand, possible ways to realize this thought experiment have been presented in the literature, although this will not be our focus now. In the following, we propose the demarcation of the Maxwell's demon experiment as a system, indicating what this particular system, its PF, and its conditions of existence are as such.
1 PS (a) Structural components: a completely isolated box with a door that can open and close in an ideal way, (b) operating components: the demon who controls the door; and (c) flow components: a gas with equal temperature composed of molecules moving at different speeds.
2 PF Decrease the entropy of the system assuming no exchange of energy between it and its outside.
3 C1 It is physically possible to decrease the entropy of an isolated system (i.e. violating the second law of thermodynamics).
4 C2 The demon needs to know the velocity of the particles, their positions, and the sides that are associated with “cold” and “hot” states in order to control the door without using energy aiming at a decrease in the system entropy.
5 C3 The system has no relation to the environment (no flow of energy, matter, or information); therefore, this condition can be excluded.
2.5.2 Classification
The Maxwell's demon experiment is a human‐made conceptual dynamic closed system. It is human made because this thought experiment only exists as a human‐made theoretical construction. In this case, it is a conceptual system because it does not have a material realization. If we consider an experiment proposed in [12], then we would have a material system; this case will be analyzed later on. The system is dynamic because it changes its states over time. It is interesting to note that there are two interrelated levels with respect to the system dynamics: (i) system‐level considering variations in macrostate properties like temperature or entropy, or (ii) molecular‐level considering the movements of the molecules; these microstates are related to, for example, their individual velocity or position. The interrelation between the macrostates and the microstates is of extreme importance and will be presented in the next chapter, where we will focus on uncertainty. By definition, Maxwell's demon is an isolated system without any in‐ and outflows, and therefore, it is a closed system.
2.5.3 Discussions
Maxwell's demon is a theoretical construction, but it can be unambiguously defined as a system. The proposed demarcation indicates potential ways to actually build a material system that realizes the thought experiment. For example, the experiment presented in [12] defines a realization of the Maxwell's demon system based on electronics (single electron transistors). A careful analysis will show that such a material system maintains the basic features of the conceptual one, but with key differences that might be revealed by the demarcation of the actual experimental setup with its own limitations. In this case, the proposed demarcation is helpful either to design material realizations of a theoretical construction or to compare a physical experiment with the concept it aims to realize.
Another interesting point is about its PF and respective conditions of production. How is it possible to produce a function that does not respect a fundamental law of physics? A harsh answer would be that this system cannot exist, and thus, there is no need to discuss such a metaphysical construction in physics. We argue that the key issue here is the name given to the operating component: demon or a supernatural being. Its attribute is to open and close the door based on the knowledge of microstates of the system (velocity and location of molecules), and it has a specific goal of separating fast molecules to one side and slow to another – the hot and cold side, respectively. This split of the flow component based on its microstates into two different macrostates (hot and cold) leads to