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Physical Review E

Parity effect and phase transitions in quantum Szilard engines

Yao Lu, Gui Lu Long

Published Jan 17, 2012• 21 citations
Publisher

Abstract

Quantum Szilard engines with an arbitrary number of identical particles are studied in this paper. Analytical expressions for the total work in the low- and high-temperature limits are obtained. The total work depends on both the particle statistics, the odd-even parity, and the temperature of the system. The parity effect is drastic in fermion systems. An odd number of fermions perform work as if they were a single fermion, and an even number of fermions do not perform any work at all. For bosons, there exists a phase transition at a critical temperature under which work done by the engine is always negative. It is found that only above a certain temperature, bosonic quantum Szilard engine does more work than fermionic one. The possible experimental verification of these effects is discussed.

DOI
10.1103/physreve.85.011125

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Quantum Szilard Engine

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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.

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Quantum Szilard engines with an arbitrary number of identical particles are studied in this paper. Analytical expressions for the total work in the low- and high-temperature limits are obtained. The total work depends on both the particle statistics, the odd-even parity, and the temperature of the system. The parity effect is drastic in fermion systems. An odd number of fermions perform work as if they were a single fermion, and an even number of fermions do not perform any work at all. For bosons, there exists a phase transition at a critical temperature under which work done by the engine is always negative. It is found that only above a certain temperature, bosonic quantum Szilard engine does more work than fermionic one. The possible experimental verification of these effects is discussed.
The quantum Szilard engine (QSZE) is a conceptual quantum engine for understanding the fundamental physics of quantum thermodynamics and information physics. We generalize the QSZE to an arbitrary spin case, i.e., a spin QSZE (SQSZE), and we systematically study the basic physical properties of both fermion and boson SQSZEs in a low-temperature approximation. We give the analytic formulation of the total work. For the fermion SQSZE, the work might be absorbed from the environment, and the change rate of the work with temperature exhibits periodicity and even-odd oscillation, which is a generalization of a spinless QSZE. It is interesting that the average absorbed work oscillates regularly and periodically in a large-number limit, which implies that the average absorbed work in a fermion SQSZE is neither an intensive quantity nor an extensive quantity. The phase diagrams of both fermion and boson SQSZEs give the SQSZE doing positive or negative work in the parameter space of the temperature and the particle number of the system, but they have different behaviors because the spin degrees of the fermion and the boson play different roles in their configuration states and corresponding statistical properties. The critical temperature of phase transition depends sensitively on the particle number. By using Landauer's erasure principle, we give the erasure work in a thermodynamic cycle, and we define an efficiency (we refer to it as information-work efficiency) to measure the engine's ability of utilizing information to extract work. We also give the conditions under which the maximum extracted work and highest information-work efficiencies for fermion and boson SQSZEs can be achieved.
The Szilard engine is the simplest possible engine, composed only of one or more particles in a box. The box is then immersed in a heat bath and partitioned into two parts by a wall. It is known that in the cold temperature limit, one may extract more work out of elementary boson than out of elementary fermions. In this paper, we consider the amount of work that can be extracted out of a system of composite particles -- particles which are composed of two interacting elementary fermions of different species. We demonstrate that the amount of work extracted is closely tied to the amount of entanglement within the composite particles
In this thesis, different aspects of the quantum Szilard engine are studied using the configuration interaction method. The engine is modelled as a one-dimensional infinite well. The effects of a contact-interaction are examined and it is found that attractive contact-interactions can improve the work output at certain temperatures of an engine that has bosons as a working medium. The role of impurities in the engine is investigated and found to have a large impact on the low-temperature behaviour of the engine. Dynamics of a single-particle engine are considered in order to identify finite-speed effects in the engine's cycle.
Abstract In this article, we have realized the quantum Szilard engine (QZE) for non-interacting bosons. We have adopted the Bose–Einstein statistics for this purpose. We have considered fractional power law potential for this purpose and have used the artifact of the quantization of energy. We have calculated the work and the efficiency for non-interacting bosons in fractional power potential. We have shown the dependence of the number of particles for the work and the efficiency. We also have realized the QZE for a single-particle in a Morse potential revealing how the depth of the potential impacts both work and efficiency. Furthermore, we have examined the influence of temperature and the anharmonicity parameter on the work. Finally, we have conducted a comparative analysis, considering both non-interacting bosons in a fractional power law potential and a single-particle in a Morse potential under harmonic approximation conditions.
In this article, we have realized the quantum Szilard engine (QZE) for non-interacting bosons. We have adopted the Bose-Einstein statistics for this purpose. We have considered fractional power law potential for this purpose and have used the artifact of the quantization of energy. We have calculated the work and the efficiency for non-interacting bosons in fractional power potential. We have shown the dependence of the number of particles for the work and the efficiency. We also have realized the QZE for a single-particle in a Morse potential revealing how the depth of the potential impacts both work and efficiency. Furthermore, we have examined the influence of temperature and the anharmonicity parameter on the work. Finally, we have conducted a comparative analysis, considering both non-interacting bosons in a fractional power law potential and a single-particle in a Morse potential under harmonic approximation conditions.
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.