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arXiv:quant-ph/9612034 · Physical Review A

Quantum-mechanical Maxwell’s demon

Seth Lloyd

Published Nov 1, 1997• 235 citations
arXivHTMLPDF

Abstract

A Maxwell's demon is a device that gets information and trades it in for thermodynamic advantage, in apparent (but not actual) contradiction to the second law of thermodynamics. Quantum-mechanical versions of Maxwell's demon exhibit features that classical versions do not: in particular, a device that gets information about a quantum system disturbs it in the process. This paper proposes experimentally realizable models of quantum Maxwell's demons, explicates their thermodynamics, and shows how the information produced by quantum measurement and by decoherence acts as a source of thermodynamic inefficiency.

DOI
10.1103/physreva.56.3374

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A Maxwell's demon is a device that gets information and trades it in for thermodynamic advantage, in apparent (but not actual) contradiction to the second law of thermodynamics. Quantum-mechanical versions of Maxwell's demon exhibit features that classical versions do not: in particular, a device that gets information about a quantum system disturbs it in the process. This paper proposes experimentally realizable models of quantum Maxwell's demons, explicates their thermodynamics, and shows how the information produced by quantum measurement and by decoherence acts as a source of thermodynamic inefficiency.
Maxwell's demon explores the role of information in physical processes.Employing information about microscopic degrees of freedom, this "intelligent observer" is capable of compensating entropy production (or extracting work), apparently challenging the second law of thermodynamics.In a modern standpoint, it is regarded as a feedback control mechanism and the limits of thermodynamics are recast incorporating information-to-energy conversion.We derive a trade-off relation between information-theoretic quantities empowering the design of an efficient Maxwell's demon in a quantum system.The demon is experimentally implemented as a spin-1=2 quantum memory that acquires information, and employs it to control the dynamics of another spin-1=2 system, through a natural interaction.Noise and imperfections in this protocol are investigated by the assessment of its effectiveness.This realization provides experimental evidence that the irreversibility in a nonequilibrium dynamics can be mitigated by assessing microscopic information and applying a feed-forward strategy at the quantum scale.
Maxwell's demon explores the role of information in physical processes. Employing information about microscopic degrees of freedom, this "intelligent observer" is capable of compensating entropy production (or extracting work), apparently challenging the second law of thermodynamics. In a modern standpoint, it is regarded as a feedback control mechanism and the limits of thermodynamics are recast incorporating information-to-energy conversion. We derive a trade-off relation between information-theoretic quantities empowering the design of an efficient Maxwell's demon in a quantum system. The demon is experimentally implemented as a spin-1/2 quantum memory that acquires information, and employs it to control the dynamics of another spin-1/2 system, through a natural interaction. Noise and imperfections in this protocol are investigated by the assessment of its effectiveness. This realization provides experimental evidence that the irreversibility in a nonequilibrium dynamics can be mitigated by assessing microscopic information and applying a feed-forward strategy at the quantum scale.
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.
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.
Information thermodynamics is a generalization of thermodynamics to quantum systems and includes information as an analogy of negative entropy. This leads to a generalization of the second law in which the presence of quantum information is taken into account. Whether this information corresponds to conscious information, is left open. In an article published by Minagawa et al in Nature, a more rigorous proof than before is represented for the statement that the second law of thermodynamics is also valid in quantum theory with information included. The presence of information makes possible an apparent local violation of the second law in the sense that the system can do more work than the Carnot law allows. However, Maxwell's demon requires metabolic energy to function and it loses it when demonizing. This energy must be compensated and the conclusion is that the second law of thermodynamics is valid.
The second law of thermodynamics states that the entropy of a closed system is nondecreasing. Discussing the second law in the quantum world poses different challenges and provides different opportunities, involving fundamental quantum-information-theoretic questions and interesting quantum-engineered devices. In quantum mechanics, systems with an evolution described by a so-called unital quantum channel evolve with a nondecreasing entropy. Here, we seek the opposite, a system described by a nonunital and, furthermore, energy-conserving channel that describes a system whose entropy decreases with time. We propose a setup involving a mesoscopic four-lead scatterer augmented by a microenvironment in the form of a spin that realizes this goal. Within this nonunital and energy-conserving quantum channel, the microenvironment acts with two noncommuting operations on the system in an autonomous way. We find that the process corresponds to a partial exchange or swap between the system and environment quantum states, with the system's entropy decreasing if the environment's state is more pure. This entropy-decreasing process is naturally expressed through the action of a quantum Maxwell demon and we propose a quantum-thermodynamic engine with four qubits that extracts work from a single heat reservoir when provided with a reservoir of pure qubits. The special feature of this engine, which derives from the energy conservation in the nonunital quantum channel, is its separation into two cycles, a working cycle and an entropy cycle, allowing us to run this engine with no local waste heat.