Quantum Szilard Engine Research Articles

Finite-time optimization of a quantum Szilard heat engine

We propose a finite-time quantum Szilard engine (QSE) with a spin-1/2 quantum particle as the working substance (WS) to accelerate the operation of information engines. We introduce a Maxwell's demon (MD) to probe the spin state within a finite measurement time tM to capture the which-way information of the particle, quantified by the mutual information I(tM) between WS and MD. We establish that the efficiency η of QSE is bounded by η≤1−(1−ηC)ln2/I(tM), where I(tM)/ln2 characterizes the ideality of quantum measurement, and approaches 1 for the Carnot efficiency reached under ideal measurement in quasistatic regime. We find that the output power of QSE scales as PO∝tM3 in the short-time regime and as PO∝tM−1 in the long-time regime. Additionally, considering the energy cost for erasing the MD's memory required by Landauer's principle, there exists a threshold time that guarantees QSE to output positive work. Published by the American Physical Society 2024

Study of quantum Szilard engine for non-interacting bosons in fractional power-law potentials

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.

Influence of the seed of measurement on the work extracted in a quantum Szilard engine

We investigate the influence of the seed of measurement on the performance of a Szilard engine based on a two-mode Gaussian state evolving in a noisy channel. Quantum work is extracted by performing a positive operator-valued measurement (POVM) on one of the two modes, after which this mode reaches equilibrium with the environment. As the seed of measurement, we use a single-mode squeezed thermal state. We employ the Markovian Kossakowski-Lindblad master equation to determine the evolution in time of the considered open system and the quantum work is defined based on the Rényi entropy of order 2. We show that the extracted quantum work and information-work efficiency strongly depend on the characteristic parameters of the system (frequency, average thermal photons number, and squeezing), the noisy channel (temperature and squeezing of the bath), and the seed of measurement (average thermal photons number and strength of the measurement).

The optimal Maxwell's demon in quantum Szilard engine

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.

Landauer's Principle in a Quantum Szilard Engine without Maxwell's Demon.

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.

Deep reinforcement learning for quantum Szilard engine optimization

Machine learning techniques based on artificial neural networks have been successfully applied to solve many problems in science. One of the most interesting domains of machine learning, reinforcement learning, has natural applicability for optimization problems in physics. In this work we use deep reinforcement learning and Chopped Random Basis optimization, to solve an optimization problem based on the insertion of an off-center barrier in a quantum Szilard engine. We show that using designed protocols for the time dependence of the barrier strength, we can achieve an equal splitting of the wave function (1/2 probability to find the particle on either side of the barrier) even for an asymmetric Szilard engine in such a way that no information is lost when measuring which side the particle is found. This implies that the asymmetric non-adiabatic Szilard engine can operate with the same efficiency as the traditional Szilard engine, with adiabatic insertion of a central barrier. We compare the two optimization methods, and demonstrate the advantage of reinforcement learning when it comes to constructing robust and noise-resistant protocols.

Entropy Distribution in a Quantum Informational Circuit of Tunable Szilard Engines

This paper explores the possibility of extending the existing model of a single-particle Quantum Szilard Engine to take advantage of some features of quantum information for driving typical mechanical systems. It focuses on devices that output mechanical work, extracting energy from a single thermal reservoir at the cost of increasing the entropy of a qubit; the reverse process is also considered. In this alternative, several engines may share the information carried by the same qubit, although its interception will prove completely worthless for any illegitimate user. To this end, multi-partite quantum entanglement is employed. Besides, some changes in the cycle of the standard single-particle Quantum Szilard Engine are described, which lend more flexibility to meeting additional requirements in typical mechanical systems. The modifications allow having qubit input and output states of adjustable entropy. This feature enables the possibility of chaining the qubit between engines so that its output state from one can be used as an input state for another. Finally, another tweak is presented that allows for tuning the average output force of the engine.

Bosonic Szilard engine assisted by Feshbach resonances

It was recently found that the information-to-work conversion in a quantum Szilard engine can be increased by using a working medium of bosons with attractive interactions. In the original scheme, the work output depends on the insertion and removal position of an impenetrable barrier that acts like a piston, separating the chambers of the engine. Here, we show that the barrier removal process can be made fully reversible, resulting in a full information-to-work conversion if we also allow for the interaction strength to change during the cycle. Hence, it becomes possible to reach the maximum work output per cycle dictated by the second law of thermodynamics. These findings can, for instance, be experimentally verified with ultra-cold atoms as a working medium, where a change of interaction strength can be controlled by Feshbach resonances.

A quantum Szilard engine without heat from a thermal reservoir

We study a quantum Szilard engine that is not powered by heat drawn from a thermal reservoir, but rather by projective measurements. The engine is constituted of a system , a weight , and a Maxwell demon , and extracts work via measurement-assisted feedback control. By imposing natural constraints on the measurement and feedback processes, such as energy conservation and leaving the memory of the demon intact, we show that while the engine can function without heat from a thermal reservoir, it must give up at least one of the following features that are satisfied by a standard Szilard engine: (i) repeatability of measurements; (ii) invariant weight entropy; or (iii) positive work extraction for all measurement outcomes. This result is shown to be a consequence of the Wigner–Araki–Yanase theorem, which imposes restrictions on the observables that can be measured under additive conservation laws. This observation is a first-step towards developing ‘second-law-like’ relations for measurement-assisted feedback control beyond thermality.

Optimal work of the quantum Szilard engine under isothermal processes with inevitable irreversibility

We have found the optimal conditions for work performed by the quantum Szilard engine (SZE) containing multi-particles under isothermal processes with inevitable irreversibility. We define the restorability as the probability that the reversibility of an engine with inevitable irreversibility is achieved when the time-backward process is performed. The optimal condition is then obtained when the restorability is maximized. This is equivalent to the condition that the time-forward force is equal to the time-backward force. We numerically confirm our expectation by using the quantum SZE containing three bosons or fermions.

Quantum Szilard engines with arbitrary spin.

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.

Szilard’s information heat engines in the deep quantum regime

We investigate Szilard’s information heat engine in the deep quantum regime. If the ground state is non-degenerate, the work extracted from the engine divided by temperature, ~S, vanishes as the temperature approaches zero, where the third law of thermodynamics manifests itself in information science. The degenerate ground state induced by the symmetry or by accident gives rise to non-zero ~S at zero temperature. Based upon these two rules, namely the third law and the degenerate ground state, we can understand the low-temperature behavior of the quantum Szilard engine in various physical situations such as an engine consisting of either bosons or fermions either with or without interactions.

Revisiting the quantum Szilard engine with fully quantum considerations

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→∞ or the temperature of the bath T→∞ the QSZE reduces to the classical Szilard engine (CSZE), and the total work satisfies the relation Wtot=kBTln2 as obtained by Sang Wook Kim et al. [S.W. Kim, T. Sagawa, S. De Liberato, M. Ueda, Phys. Rev. Lett. 106 (2011) 070401] for one particle case.

Multiparticle quantum Szilard engine with optimal cycles assisted by a Maxwell's demon

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.

Parity effect and phase transitions in quantum Szilard engines

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.

Quantum Szilard Engine

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.