Читать книгу Cyber-physical Systems - Pedro H. J. Nardelli - Страница 33

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 a decrease in the system entropy, which is the aim of the system. In today's terminology, Maxwell's demon could be renamed an ideal smart controller.

Clearly, with the knowledge and technology available in the nineteenth century, as well as the general context back then, defining the problem as a thought experiment in reference to a demon is understandable. The proposed change of name is an index that the demon is a computing device that is internal to the closed system. Since computing has its own fundamental laws related dissipation of energy as demonstrated by Landauer in [13], this result indicates that the Maxwell's demon experiment cannot form an isolated system because of the fundamental limits of computation. Therefore, the second law remains valid, and the Maxwell's demon experiment cannot exist as a system whose function is to decrease the entropy of an isolated system.

Given this, we can rectify our demarcation of Maxwell's demon as follows.

1 PS (a) Structural components: a completely isolated box with a door that can open and close in an ideal way, (b) operating components: an ideal smart controller which 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 through necessary computing processes assuming no exchange of energy between it and its outside except by the unavoidable dissipation related to computing processes.

3 C1 It is physically possible to decrease the entropy of an isolated system without violating the second law of thermodynamics by utilizing necessary computing processes.

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. These are the computing processes.

5 C3 The system has no relation to the environment (no flow of energy, matter, or information) except by the fundamental heat generation related to the necessary computing processes.

In this way, the conceptual system is posed in scientific terms that allow for experimentation by its material realization. As the result presented in [12] demonstrates, this thought experiment can be materially realized. However, we are not yet done with the Maxwell's demon experiment because of its relations to uncertainty, information, and decision‐making: all topics related to the following chapters! The demon will stay with us for a while more.