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arXiv:1502.00439 · Physical Review E

Quantum Szilard engines with arbitrary spin

Zekun Zhuang, Shi‐Dong Liang

Published Nov 12, 2014• 24 citations

Abstract

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.

DOI: 10.1103/physreve.90.052117

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By considering level shifting during the insertion process we revisit the quantum Szilard engine (QSZE) with fully quantum consideration. We derive the general expressions of the heat absorbed from thermal bath and the total work done to the environment by the system in a cycle with two different cyclic strategies. We find that only the quantum information contributes to the absorbed heat, and the classical information acts like a feedback controller and has no direct effect on the absorbed heat. This is the first demonstration of the different effects of quantum information and classical information for extracting heat from the bath in the QSZE. Moreover, when the well width $L\rightarrow \infty $ or the temperature of the bath $T\rightarrow \infty $ the QSZE reduces to the classical Szilard engine (CSZE), and the total work satisfies the relation

W_{\mathtt{tot}}=k_{B}T \mathtt{ln}2

as obtained by Sang Wook Kim et al. [Phys. Rev. Lett. 106, 070401 (2011)] for one particle case.

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.

In a classic thought experiment, Szilard suggested a heat engine where a single particle, for example an atom or a molecule, is confined in a container coupled to a single heat bath. The container can be separated into two parts by a moveable wall acting as a piston. In a single cycle of the engine, work can be extracted from the information on which side of the piston the particle resides. The work output is consistent with Landauers principle that the erasure of one bit of information costs the entropy kB ln 2, exemplifying the fundamental relation between work, heat and information. Here we apply the concept of the Szilard engine to a fully interacting quantum many-body system. We find that a working medium of a number of bosons (larger or equal two) with attractive interactions is clearly superior to other previously discussed setups. In sharp contrast to the classical case, we find that the average work output increases with the particle number. The highest overshoot occurs for a small but finite temperature, showing an intricate interplay between thermal and quantum effects. We anticipate that our finding will shed new light on the role of information in controlling thermodynamic fluctuations in the deep quantum regime, which are strongly influenced by quantum correlations in interacting systems.

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 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.

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.