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arXiv:1607.00994 · Entropy

Implications of Coupling in Quantum Thermodynamic Machines

GEORGE M. THOMAS, Manik Banik, Sibasish Ghosh A

Published Sep 8, 2017• 25 citations
arXivHTMLPDF

Abstract

We study coupled quantum systems as the working media of thermodynamic machines. Under a suitable phase-space transformation, the coupled systems can be expressed as a composition of independent subsystems. We find that for the coupled systems, the figures of merit, that is the efficiency for engine and the coefficient of performance for refrigerator, are bounded (both from above and from below) by the corresponding figures of merit of the independent subsystems. We also show that the optimum work extractable from a coupled system is upper bounded by the optimum work obtained from the uncoupled system, thereby showing that the quantum correlations do not help in optimal work extraction. Further, we study two explicit examples; coupled spin- 1 / 2 systems and coupled quantum oscillators with analogous interactions. Interestingly, for particular kind of interactions, the efficiency of the coupled oscillators outperforms that of the coupled spin- 1 / 2 systems when they work as heat engines. However, for the same interaction, the coefficient of performance behaves in a reverse manner, while the systems work as the refrigerator. Thus, the same coupling can cause opposite effects in the figures of merit of heat engine and refrigerator.

DOI
10.3390/e19090442

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We study coupled quantum systems as the working media of thermodynamic machines. Under a suitable phase-space transformation, the coupled systems can be expressed as a composition of independent subsystems. We find that for the coupled systems, the figures of merit, that is the efficiency for engine and the coefficient of performance for refrigerator, are bounded (both from above and from below) by the corresponding figures of merit of the independent subsystems. We also show that the optimum work extractable from a coupled system is upper bounded by the optimum work obtained from the uncoupled system, thereby showing that the quantum correlations do not help in optimal work extraction. Further, we study two explicit examples; coupled spin- 1 / 2 systems and coupled quantum oscillators with analogous interactions. Interestingly, for particular kind of interactions, the efficiency of the coupled oscillators outperforms that of the coupled spin- 1 / 2 systems when they work as heat engines. However, for the same interaction, the coefficient of performance behaves in a reverse manner, while the systems work as the refrigerator. Thus, the same coupling can cause opposite effects in the figures of merit of heat engine and refrigerator.
In this work, we study coupled quantum systems as working media of thermodynamic machines. With suitable co-ordinate transformation, the coupled system appears to be uncoupled in the new frame of reference. In that case, the global efficiency of the total system is bounded (both from above and below) by the efficiencies of the independent subsystems, provided both the independent subsystems work in the engine mode. This is also true for the coefficient of performance when the coupled system behave as refrigerator. We make a comparative study between coupled spin-1/21/21/2 systems and coupled quantum oscillators considering analogous interaction for both the systems. Interestingly, for particular kind of interactions, the efficiency of the coupled oscillators outperforms that of the coupled spin-1/21/21/2 systems when they work as heat engines. However, for same interaction, the coefficient of performance behaves in a reverse manner, while the system work as refrigerator. Therefore coupling can cause opposite effects in the figure of merits of heat engine and refrigerator.
Study of coupled quantum systems as quantum heat engines is an interesting research area. It has been shown earlier that coupling can increase the efficiency. Here we make a comparative study between coupled spin-1/21/21/2 systems and coupled quantum oscillators when they constitute as the working medium of a quantum heat engine. For this purpose, we consider anisotropic 1-D Heisenberg model of interaction between two spin-1/21/21/2 systems. Analogous interaction in the case of two oscillators is realized by considering quadratic coupling between positions and momenta of the two oscillators. Interestingly, we point out certain range of parameters for which the efficiency of the coupled oscillators outperform the efficiency obtained from coupled spin systems. It happens that with suitable co-ordinate transformation, the coupled system appears to be uncoupled in the new frame of reference. We show that the global efficiency of the total system is bounded (both from above and below) by the efficiencies of the independent systems, provided both the independent systems work in the engine mode. When the upper bound of the efficiency becomes Carnot efficiency, then the global efficiency reaches the lower bound. The global efficiency further decreases when one of the independent systems works as a refrigerator.
Abstract We start with a revision study of two coupled spin- 1 / 2 under the influence of Kaplan–Shekhtman–Entin-Wohlman–Aharony interaction and a magnetic field. We first show the role of idle levels, i.e. levels that do not couple to the external magnetic field, when the system is working as a heat engine as well as when it is a refrigerator. Then we extend the results reported in Altintas and Müstecaplıoğlu (2015 Phys. Rev. E 92 022142) by showing that it is not necessary to change both the magnetic field as well as the coupling parameters to break the extensive property of the work extracted globally from two coupled spin- 1 / 2 as has been demonstrated there. Then we study the role of increasing the number of coupled spins on efficiency, extractable work, and coefficient of performance (COP). First, we consider two- and three-coupled spin- 1 / 2 Heisenberg X X X -chain. We prove that the latter can outperform the former in terms of efficiency, extractable work, and COP. Then we consider the Ising model, where the number of interacting spins ranges from two to six. We show that only when the number of interacting spins is odd the system can work as a heat engine in the strong coupling regime. The enhancements in efficiency and COP are explored in detail. Finally, this model confirms the idea that entanglement and quantum correlations are not the reasons behind the enhancements observed in efficiency, extractable work, and COP, but only due to the structure of the energy levels of the Hamiltonian of the working substance. In addition to this, the extensive property of global work as well, is not affected by entanglement and quantum correlations.
The study of quantum thermodynamics is key to the development of quantum thermal machines. Here we investigate a system of parametrically driven quantum harmonic oscillators coupled to heat baths via a collision model. Using a thermodynamically consistent local master equation, we derive the heat flows and work power of the working device which can operate as an engine or a refrigerator and analyse their instantaneous and averages efficiencies and coefficients of performance. Studying the regimes of both slow and fast driving of the system, we find that an increased driving frequency can lead to a change of functioning to an accelerator or a heater. Finally, we investigate the effect of squeezing one of the thermal baths: it leads to an apparent higher efficiency compared to the corresponding Carnot value of an equilibrium bath with the same temperature and to sustained entanglement between the working substance oscillators in the limit cycle.
The minimal-coupling quantum heat engine is a thermal machine consisting of an explicit energy storage system, heat baths, and a working body, which alternatively couples to subsystems through discrete strokes --- energy-conserving two-body quantum operations. Within this paradigm, we present a general framework of quantum thermodynamics, where a work extraction process is fundamentally limited by a flow of non-passive energy (ergotropy), while energy dissipation is expressed through a flow of passive energy. It turns out that small dimensionality of the working body and a restriction only to two-body operations make the engine fundamentally irreversible. Our main result is finding the optimal efficiency and work production per cycle within the whole class of irreversible minimal-coupling engines composed of three strokes and with the two-level working body, where we take into account all possible quantum correlations between the working body and the battery. One of the key new tools is the introduced ``control-marginal state" --- one which acts only on a working body Hilbert space, but encapsulates all features regarding work extraction of the total working body-battery system. In addition, we propose a generalization of the many-stroke engine, and we analyze efficiency vs extracted work trade-offs, as well as work fluctuations after many cycles of the running of the engine.
The laws of thermodynamics put limits to the efficiencies of thermal machines. Analogues of these laws are now established for quantum engines weakly and passively coupled to the environment providing a framework to find improvements to their performance. Systems whose interaction with the environment is actively controlled do not fall in that framework. Here we consider systems actively and locally coupled to the environment, evolving with a so-called boundary-driven Lindblad equation. Starting from a unitary description of the system plus the environment we simultaneously obtain the Lindblad equation and the appropriate expressions for heat, work and entropy-production of the system extending the framework for the analysis of new, and some already proposed, quantum heat engines. We illustrate our findings in spin 1/2 chains and explain why an XX chain coupled in this way to a single heat bath relaxes to thermodynamic-equilibrium while and XY chain does not. Additionally, we show that an XX chain coupled to a left and a right heat baths behaves as a quantum engine, a heater or refrigerator depending on the parameters, with efficiencies bounded by Carnot efficiencies.