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Maxwell's demon in quantum mechanics : Simulation of a quantum wave packet in a two-dimensional double cavity system

Matias Mustonen

Published Jan 1, 2020• 0 citations
OpenAlex

Abstract

Maxwell’s demon is a thought experiment in which the second rule of thermodynamics is violated. Originally, the thought experiment consisted of two connected cavities with a filter betweenthem. The demon could choose to let particles go through the connection gap. If the demonwere to let faster moving particles to one cavity and slower moving particles to the other cavity itwould introduce a temperature difference in the system. Thus, decreasing the total entropy of thesystem violating the second rule of thermodynamics.In classical mechanics the experiment can be implemented as a two-dimensional two-cavitysystem, where one cavity is integrable and the other is chaotic. The probability for a particleto travel from the chaotic cavity to the integrable is greater than vice versa. This creates animbalance in an observable such as pressure.In this thesis we investigate the quantum mechanical counterpart of the classical double cavitywith one cavity being an integrable rectangle and the other one a chaotic stadium. We initialize thesystem with a quantum mechanical wave packet in one of the cavities and compute the system’stime-evolution. The time-evolution is analyzed with visualizations of the probability density and byinspecting observables related to the system’s ergodic properties such as autocorrelation, inverseparticipation ratio, and information entropy.If initialized in the chaotic cavity, we have found that the wave packet propagates much fasterto the other cavity than if it was initially in the regular cavity. This is a quantum mechanicaldemonstration of the original Maxwell’s thought experiment.

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Maxwell’s demon is a thought experiment in which the second rule of thermodynamics is violated. Originally, the thought experiment consisted of two connected cavities with a filter betweenthem. The demon could choose to let particles go through the connection gap. If the demonwere to let faster moving particles to one cavity and slower moving particles to the other cavity itwould introduce a temperature difference in the system. Thus, decreasing the total entropy of thesystem violating the second rule of thermodynamics.In classical mechanics the experiment can be implemented as a two-dimensional two-cavitysystem, where one cavity is integrable and the other is chaotic. The probability for a particleto travel from the chaotic cavity to the integrable is greater than vice versa. This creates animbalance in an observable such as pressure.In this thesis we investigate the quantum mechanical counterpart of the classical double cavitywith one cavity being an integrable rectangle and the other one a chaotic stadium. We initialize thesystem with a quantum mechanical wave packet in one of the cavities and compute the system’stime-evolution. The time-evolution is analyzed with visualizations of the probability density and byinspecting observables related to the system’s ergodic properties such as autocorrelation, inverseparticipation ratio, and information entropy.If initialized in the chaotic cavity, we have found that the wave packet propagates much fasterto the other cavity than if it was initially in the regular cavity. This is a quantum mechanicaldemonstration of the original Maxwell’s thought experiment.
Maxwell's Demon is a thought experiment devised by J. C. Maxwell in 1867 in order to show that the Second Law of thermodynamics is not universal, since it has a counter-example. Since the Second Law is taken by many to provide an arrow of time, the threat to its universality threatens the account of temporal directionality as well. Various attempts to "exorcise" the Demon, by proving that it is impossible for one reason or another, have been made throughout the years, but none of them were successful. We have shown (in a number of publications) by a general state-space argument that Maxwell's Demon is compatible with classical mechanics, and that the most recent solutions, based on Landauer's thesis, are not general. In this paper we demonstrate that Maxwell's Demon is also compatible with quantum mechanics. We do so by analyzing a particular (but highly idealized) experimental setup and proving that it violates the Second Law. Our discussion is in the framework of standard quantum mechanics; we give two separate arguments in the framework of quantum mechanics with and without the projection postulate. We address in our analysis the connection between measurement and erasure interactions and we show how these notions are applicable in the microscopic quantum mechanical structure. We discuss what might be the quantum mechanical counterpart of the classical notion of "macrostates", thus explaining why our Quantum Demon setup works not only at the micro level but also at the macro level, properly understood. One implication of our analysis is that the Second Law cannot provide a universal lawlike basis for an account of the arrow of time; this account has to be sought elsewhere.
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.
"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
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.
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
In apparent contradiction to the laws of thermodynamics, Maxwell's demon is able to cyclically extract work from a system in contact with a thermal bath, exploiting the information about its microstate. The resolution of this paradox required the insight that an intimate relationship exists between information and thermodynamics. Here, we realize a Maxwell demon experiment that tracks the state of each constituent in both the classical and quantum regimes. The demon is a microwave cavity that encodes quantum information about a superconducting qubit and converts information into work by powering up a propagating microwave pulse by stimulated emission. Thanks to the high level of control of superconducting circuits, we directly measure the extracted work and quantify the entropy remaining in the demon's memory. This experiment provides an enlightening illustration of the interplay of thermodynamics with quantum information.