To test the universality of the Second Law of Thermodynamics from the position of his “mechanical” theory of gas, James Clerk Maxwell invented a being capable to manipulate with individual molecules in an artful manner. He placed this Demon into a box divided by a partition with a weightless window and charged him with duty to be a gatekeeper. Both sides of the partition were full of gas initially at one common temperature. According to the microscopic theory of temperature, there was a large spread of speed of molecules, even though the average temperatures were equal. The task of the Demon was to open the window for the fast molecules moving from the right chamber to the left one. To keep the number of molecules in both chambers equal, he let pass the slow molecules from the left to right chamber.
To test the universality of the Second Law of Thermodynamics from the position of his “mechanical” theory of gas, James Clerk Maxwell invented a being capable to manipulate with individual molecules in an artful manner. He placed this Demon into a box divided by a partition with a weightless window and charged him with duty to be a gatekeeper. Both sides of the partition were full of gas initially at one common temperature. According to the microscopic theory of temperature, there was a large spread of speed of molecules, even though the average temperatures were equal. The task of the Demon was to open the window for the fast molecules moving from the right chamber to the left one. To keep the number of molecules in both chambers equal, he let pass the slow molecules from the left to right chamber.
According to (1) and (2), no work is done by Maxwell’s demon who knows the speed of molecules in a gas and opens a door in the wall to allow fast molecules into a second empty chamber. Thus, one has cold molecules in one chamber and hot, in the other, “seemingly without applying any work” (1). In other words, the second law of thermodynamics is violated because entropy decreases without work being done. The 2018 paper (2), also states that no work is done in such a situation. We argue that a number of different types of work or energy expenditure are required by the demon. First of all, position and time measurements of a molecule must be made before a speed calculation can be taken. In principle, this information must be acquired and stored, either in an electronic form, some kind of writing or in a brain and this requires energy/work. Next, a calculation of speed must be made and this again requires work. Then energy is required to make the decision whether the speed meets a certain threshold and energy is required to remove the data from memory. In addition, work must be done in opening the door for each fast molecule. The door does not open without work being performed because it must move and so requires a force by Newton’s laws. The force acts over a distance and then the force must be applied in the opposite direction so work again is done. Even if there is very little friction in the system and the force is tiny as well as the distance, some work must be done. Furthermore, there are time issues as the door must be opened very quickly and then closed quickly, so vf-0 = acceleration * t and distance = .5*acceleration*tt applies. A certain speed vf must be reached and if t is tiny, acceleration cannot tend to 0 and acceleration is then multiplied by mass. As a result, it seems curious that statements about no work are made in the literature (1), (2). As an example of a system which bypasses the demon, but accomplishes the same goal as Maxwell’s demon, one may see that work is required. It is possible to create two tunnels one after the other to play the role of the demon. There is a potential hindering motion in the first tunnel. Only partilces with kinetic energy greater than some limit V1 reach the end of the first tunnel. The rest come to a stop and then are accelerated back to their original speed, but move in the opposite direction. The ones that reach the end of the first tunnel are then pulled by a force in the second tunnel which restores kinetic energy of V1 and so they exit the second tunnel with their original speed and enter a second tunnel. One may see that in this example which replaces Maxwell’s demon that work is done and even calculate the exact amount.
This chapter introduces the thermodynamics of information, a concept that finds wide use in physics and astrophysics. The link between physics and information began in 1867, with James Clerk Maxwell's thought experiment of a creature capable of beating the second law of thermodynamics. Entropy can therefore be said to represent the missing information about a system that can't be accounted for in macroscopic descriptions; the larger the entropy, the more the missing information. When Maxwell introduced the demon, the distribution of speeds of the atoms of a gas at a fixed temperature had only recently been established . The demon dies an entropic death because it must discard information previously collected. One may reasonably assume that a measurement procedure is fundamentally associated with a certain definite average entropy production, and that this restores concordance with the second law. The physicist Leo Szilard undertook a careful examination of the role played by the involvement of an observer.
Demon, the famous thought experiment of James Clerk Maxwell, has been devised in 1867 as a counter example for the Second Law of thermodynamics. During the 140 years since the Demon was first suggested, numerous attempts have been made to counter Maxwell's argument. The attempts have been to show that Maxwell was wrong, since his Demon cannot work for one reason or another (see Leff and Rex 2003 for details and references). In this paper we show (following an argument by Albert 2000, Ch. 5.) that Maxwell was basically right, in the sense that his thought experiment is compatible with the laws of mechanics as well as with central principles of statistical mechanics. We then derive some (weak) restrictions on the Demon's efficiency. Finally, we prove that the Demon's cycle of operation can be completed (in particular, the Demon's memory can be erased) without increasing the total entropy of the universe. We draw some conclusions about the way to understand the meaning and role of probability in classical statistical mechanics
"Maxwell's Demon", the famous thought experiment of James Clerk Maxwell, has been devised in 1867 as a counter example for the Second Law of thermodynamics. During the 140 years since the Demon was first suggested, numerous attempts have been made to counter Maxwell's argument. The attempts have been to show that Maxwell was wrong, since his Demon cannot work for one reason or another (see Leff and Rex 2003 for details and references). In this paper we show (following an argument by Albert 2000, Ch. 5.) that Maxwell was basically right, in the sense that his thought experiment is compatible with the laws of mechanics as well as with central principles of statistical mechanics. We then derive some (weak) restrictions on the Demon's efficiency. Finally, we prove that the Demon's cycle of operation can be completed (in particular, the Demon's memory can be erased) without increasing the total entropy of the universe. We draw some conclusions about the way to understand the meaning and role of probability in classical statistical mechanics
Maxwell’s demon emanates from a thought experiment proposed by James Clerk Maxwell in 1867 to illustrate the statistical nature of the second law of thermodynamics. Subsequently researchers wondered whether such a demon could in fact violate the second law. Leon Brillouin argued that the entropy produced during the demon’s measurement precluded such a violation. Years later Oliver Penrose and Charles Bennett observed (independently) that a Maxwell’s demon gathers information and stores it in a memory. Penrose showed that erasure of such a memory sends sufficient entropy to the environment to preclude violation of the second law. Notably this is so even when measurement produces arbitrarily little entropy. Bennett obtained the same result using Rolf Landauer’s seminal research on the thermodynamics of computation. The stunning shift in focus from measurement to erasure provided the impetus to better understand the role of information in quantum mechanics and thermodynamics. Indeed the linkage of information with physics is the principal legacy of Maxwell’s demon. Szilard’s one‐particle classical “gas” model and its quantum mechanical extension, together with postulated connections between entropy and algorithmic information, have provided useful insights. We review the long history of Maxwell’s demon and assess the current status of the second law in the context of the demon’s operations.
It is nearly 150 years since Maxwell challenged the validity of the second law of thermodynamics by imagining a tiny creature who could sort the molecules of a gas in such a way that would decrease entropy without exerting any work. The demon has been discussed largely using thought experiments, but it has recently become possible to exert control over nanoscale systems, just as Maxwell imagined, and the status of the second law has become a more practical matter, raising the issue of how measurements manage our ignorance in a way that can be exploited. The framework of stochastic thermodynamics extends macroscopic concepts such as heat, work, entropy and irreversibility to small systems and allows us explore the matter. Some arguments against a successful demon imply a second law that can be suspended indefinitely until we dissipate energy in order to remove the records of his operations. In contrast, under stochastic thermodynamics, the demon fails because on average, more work is performed upfront in making a measurement than can be extracted by exploiting the outcome. This requires us to exclude systems and a demon that evolve under what might be termed self-sorting dynamics, and we reflect on the constraints on control that this implies while still working within a thermodynamic framework.