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Speculation on the Work Performed by Maxwell's Demon

Francesco R. Ruggeri

Published Jul 7, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.21240405

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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 = .5accelerationtt 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.
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.
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.
© 2016 Taylor & Francis 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.
The basic Maxwell's demon opens the gate between regions A and B when it sees a molecule moving from A to B but none moving in the opposite direction. The major standard objection to this violation of the second law of thermodynamics is that the demon would not be able to distinguish the molecules from the equilibrium background black body radiation unless it illuminated them with a beacon emitting radiation corresponding to a different temperature, thus bringing about an increase of entropy.
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.
The Second Law of thermodynamics states that the entropy of the isolated system is non-diminishing in the course of time evolution. In quantum systems, the Second Law can be violated by adding to the system the quantum Maxwell’s demon (QMD) which reduces entropy without energy exchange. However, extending the system by including into it the QMD itself, restores the Second Law. Remarkably, enlarging system with one more demon we return to the initial situation. Therefore by sequential adding the QMD, we can construct the energy-conserving macroscopic system which evolves in time with decreasing the entropy. Here we demonstrate this general principle on the IBM quantum computer how extending the system by one extra qubit, we still observe the entropy decreasing, thus violating the second law. We utilize five QMD implemented by the extra qubits since decoherence effects restrict the number of possible qubit additions.