What rate (Pd) of energy transfer is attainable by a Maxwell’s demon who sorts gas molecules serially; and how much time (td) does it take to achieve a designated temperature difference ΔT across a partition? Two estimates are made, using (i) the energy–time form of Heisenberg’s uncertainty principle and (ii) classical kinetic theory. For a dilute gas, at ∼300 K, the uncertainty principle implies Pd <1.5×10−6 W. If the gas volume is the size of a large room, and ΔT=2 K, then td >103 years. These bounds are loose, but are of interest because this is one of few elementary applications of the energy–time uncertainty principle. With similar assumptions, classical kinetic theory implies much tighter bounds: Pd <10−9 W and td >4×106 years. The kinetic theory approach allows an extension of Brillouin’s demonstration that the second law of thermodynamics cannot be violated by a Maxwell’s demon using light signals.
What rate (Pd) of energy transfer is attainable by a Maxwell’s demon who sorts gas molecules serially; and how much time (td) does it take to achieve a designated temperature difference ΔT across a partition? Two estimates are made, using (i) the energy–time form of Heisenberg’s uncertainty principle and (ii) classical kinetic theory. For a dilute gas, at ∼300 K, the uncertainty principle implies Pd <1.5×10−6 W. If the gas volume is the size of a large room, and ΔT=2 K, then td >103 years. These bounds are loose, but are of interest because this is one of few elementary applications of the energy–time uncertainty principle. With similar assumptions, classical kinetic theory implies much tighter bounds: Pd <10−9 W and td >4×106 years. The kinetic theory approach allows an extension of Brillouin’s demonstration that the second law of thermodynamics cannot be violated by a Maxwell’s demon using light signals.
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.
This work provides an overview of key historical developments in the formulation of the Second Law of Thermodynamics, focusing on the notorious challenge of ``Maxwell's Demon'', a hypothetical creature who could presumably violate that law. It begins by recalling Maxwell's challenge and discussing the apparent loophole in the Second Law that appears to make such a violation possible. An alternative formulation of the Demon challenge by Szilard is considered, along with his attempted defeat of the Demon through reference to measurement. A similar effort by Brillouin is also analyzed. The proposal of Bennett to defeat the Demon through the requirement of memory erasure is critically discussed. Finally, it is proposed that the Second Law gains a firm foundation through neglected features of quantum theory. In particular, an application of the Heisenberg Uncertainty Principle is shown to decisively defeat the Demon, as well as to serve as justification for Landauer's Principle, albeit in terms distinct from the usual computational formulation.
This work provides an overview of key historical developments in the formulation of the Second Law of Thermodynamics, focusing on the notorious challenge of “Maxwell’s Demon”, a hypothetical creature who could presumably violate that law. It begins by recalling Maxwell’s challenge and discussing the apparent loophole in the Second Law that appears to make such a violation possible. An alternative formulation of the Demon challenge by Szilard is considered, along with his attempted defeat of the Demon through reference to measurement. A similar effort by Brillouin is also analyzed. The more recent proposal of Bennett to defeat the Demon through the requirement of memory erasure is critically discussed. Finally, it is proposed that the Second Law gains a firm foundation through a neglected feature of quantum theory, namely the Heisenberg Uncertainty Principle, which also decisively serves to defeat the Demon.
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.
I dispute the conventional claim that the second law of thermodynamics is saved from a “Maxwell’s demon” by the entropy cost of information erasure and show that instead it is measurement that incurs the entropy cost. Thus, Brillouin, who identified measurement as savior of the second law, was essentially correct, and putative refutations of his view, such as Bennett’s claim to measure without entropy cost, are seen to fail when the applicable physics is taken into account. I argue that the tradition of attributing the defeat of Maxwell’s demon to erasure rather than to measurement arose from unphysical classical idealizations that do not hold for real gas molecules, as well as a physically ungrounded recasting of physical thermodynamical processes into computational and information-theoretic conceptualizations. I argue that the fundamental principle that saves the second law is the quantum uncertainty principle applying to the need to localize physical states to precise values of observables in order to effect the desired disequilibria aimed at violating the second law. I obtain the specific entropy cost for localizing a molecule in the Szilard engine and show that it coincides with the quantity attributed to Landauer’s principle. I also note that an experiment characterized as upholding an entropy cost of erasure in a “quantum Maxwell’s demon” actually demonstrates an entropy cost of measurement.