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Quantum Engineering

The optimal Maxwell's demon in quantum Szilard engine

Congyi Mou, Shuhao Cao, Tao Zhou

Published Oct 1, 2021• 1 citation
Publisher

Abstract

The quantum Szilard engine assisted by Maxwell's demon has already be discussed in complete-quantum analysis, and it is shown that the coherence assumption of Maxwell's demon is useful in quantum Szilard engine, where Maxwell's demo is a pure state. In this work, we further discuss a more practical case where Maxwell's demon is initially in contact with a heat bath, and thus a mixed state. It is shown that reference base of the quantum Maxwell's demon has an impact on the efficiency of quantum Szilard engine, and then it is of great significance to choose the optimal bases to attain the maximum efficiency. Moreover, the optimal basis and the maximum efficiency are obtained in this work.

DOI
10.1002/que2.82

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The quantum Szilard engine assisted by Maxwell's demon has already be discussed in complete-quantum analysis, and it is shown that the coherence assumption of Maxwell's demon is useful in quantum Szilard engine, where Maxwell's demo is a pure state. In this work, we further discuss a more practical case where Maxwell's demon is initially in contact with a heat bath, and thus a mixed state. It is shown that reference base of the quantum Maxwell's demon has an impact on the efficiency of quantum Szilard engine, and then it is of great significance to choose the optimal bases to attain the maximum efficiency. Moreover, the optimal basis and the maximum efficiency are obtained in this work.
We present a complete-quantum description of a multiparticle Szilard engine that consists of a working substance and a Maxwell's demon. The demon is modeled as a multilevel quantum system with specific quantum control, and the working substance consists of identical particles obeying Bose-Einstein or Fermi-Dirac statistics. In this description, a reversible scheme to erase the demon's memory by a lower-temperature heat bath is used. We demonstrate that (1) the quantum control of the demon can be optimized for a single-particle Szilard engine so that the efficiency of the demon-assisted thermodynamic cycle could reach the Carnot cycle's efficiency and (2) the low-temperature behavior of the working substance is very sensitive to the quantum statistics of the particles and the insertion position of the partition.
The Szilard engine (SZE) is the quintessence of Maxwell's demon, which can extract the work from a heat bath by utilizing information.We present the first complete quantum analysis of the SZE, and derive an analytic expression of the quantum-mechanical work performed by a quantum SZE containing an arbitrary number of molecules, where it is crucial to regard the process of insertion or removal of a wall as a legitimate thermodynamic process.We find that more (less) work can be extracted from the bosonic (fermionic) SZE due to the indistinguishability of identical particles.
We study the physical mechanism of Maxwell's demon (MD), which helps do extra work in thermodynamic cycles with the heat engine. This is exemplified with one molecule confined in an infinitely deep square potential with a movable solid wall. The MD is modeled as a two-level system (TLS) for measuring and controlling the motion of the molecule. The processes in the cycle are described in a quantum fashion. It is discovered that a MD with quantum coherence or one at a temperature lower than the molecule's heat bath can enhance the ability of the whole working substance, formed by the heat engine plus the MD, to do work outside. This observation reveals that the essential role of the MD is to drive the whole working substance off equilibrium, or equivalently, to work between two heat baths with different effective temperatures. The elaborate studies with this model explicitly reveal the effect of finite size off the classical limit or thermodynamic limit, which contradicts common sense on a Szilard heat engine (SHE). The quantum SHE's efficiency is evaluated in detail to prove the validity of the second law of thermodynamics.
The Szilard engine (SZE) is the quintessence of Maxwell's demon, which can extract the work from a heat bath by utilizing information. We present the first complete quantum analysis of the SZE, and derive an analytic expression of the quantum-mechanical work performed by a quantum SZE containing an arbitrary number of molecules, where it is crucial to regard the process of insertion or removal of a wall as a legitimate thermodynamic process. We find that more (less) work can be extracted from the bosonic (fermionic) SZE due to the indistinguishability of identical particles.
Quantum Szilard engine constitutes an adequate interplay of thermodynamics, information theory and quantum mechanics. Szilard engines are in general operated by a Maxwell's Demon where Landauer's principle resolves the apparent paradoxes. Here we propose a Szilard engine setup without featuring an explicit Maxwell's demon. In a demonless Szilard engine, the acquisition of which-side information is not required, but the erasure and related heat dissipation still take place implicitly. We explore a quantum Szilard engine considering quantum size effects. We see that insertion of the partition does not localize the particle to one side, instead creating a superposition state of the particle being in both sides. To be able to extract work from the system, particle has to be localized at one side. The localization occurs as a result of quantum measurement on the particle, which shows the importance of the measurement process regardless of whether one uses the acquired information or not. In accordance with Landauer's principle, localization by quantum measurement corresponds to a logically irreversible operation and for this reason it must be accompanied by the corresponding heat dissipation. This shows the validity of Landauer's principle even in quantum Szilard engines without Maxwell's demon.