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arXiv:1604.07557 · Physical Review A

Trading coherence and entropy by a quantum Maxwell demon

A. V. Lebedev, D. Oehri, Gordey B. Lesovik, G. Blatter

Published Nov 28, 2016• 16 citations

Abstract

The second law of thermodynamics states that the entropy of a closed system is nondecreasing. Discussing the second law in the quantum world poses different challenges and provides different opportunities, involving fundamental quantum-information-theoretic questions and interesting quantum-engineered devices. In quantum mechanics, systems with an evolution described by a so-called unital quantum channel evolve with a nondecreasing entropy. Here, we seek the opposite, a system described by a nonunital and, furthermore, energy-conserving channel that describes a system whose entropy decreases with time. We propose a setup involving a mesoscopic four-lead scatterer augmented by a microenvironment in the form of a spin that realizes this goal. Within this nonunital and energy-conserving quantum channel, the microenvironment acts with two noncommuting operations on the system in an autonomous way. We find that the process corresponds to a partial exchange or swap between the system and environment quantum states, with the system's entropy decreasing if the environment's state is more pure. This entropy-decreasing process is naturally expressed through the action of a quantum Maxwell demon and we propose a quantum-thermodynamic engine with four qubits that extracts work from a single heat reservoir when provided with a reservoir of pure qubits. The special feature of this engine, which derives from the energy conservation in the nonunital quantum channel, is its separation into two cycles, a working cycle and an entropy cycle, allowing us to run this engine with no local waste heat.

DOI: 10.1103/physreva.94.052133

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The Second Law of Thermodynamics states that temporal evolution of an isolated system occurs with non-diminishing entropy. In quantum realm, this holds for energy-isolated systems the evolution of which is described by the so-called unital quantum channel. The entropy of a system evolving in a non-unital quantum channel can, in principle, decrease. We formulate a general criterion of unitality for the evolution of a quantum system, enabling a simple and rigorous approach for finding and identifying the processes accompanied by decreasing entropy in energy-isolated systems. We discuss two examples illustrating our findings, the quantum Maxwell demon and heating-cooling process within a two-qubit system.

The Second Law of thermodynamics states that the entropy of the isolated system is non-diminishing in the course of time evolution. In quantum systems, the Second Law can be violated by adding to the system the quantum Maxwell’s demon (QMD) which reduces entropy without energy exchange. However, extending the system by including into it the QMD itself, restores the Second Law. Remarkably, enlarging system with one more demon we return to the initial situation. Therefore by sequential adding the QMD, we can construct the energy-conserving macroscopic system which evolves in time with decreasing the entropy. Here we demonstrate this general principle on the IBM quantum computer how extending the system by one extra qubit, we still observe the entropy decreasing, thus violating the second law. We utilize five QMD implemented by the extra qubits since decoherence effects restrict the number of possible qubit additions.

Subsystems of a composite system in a pure state generally exist in mixed states and undergo changes with the overall state. This phenomenon arises from the coherence of the entire system and represents a crucial distinction between quantum and classical systems. Such a quantum property can enhance the work output of an Otto heat engine composed of two qubits, whose parameters evolve in opposite directions. When the energy levels of the two qubits are identical at one of the thermal equilibrium states of the Otto cycle and there is no interaction between them, the total work output is strictly negative, which is guaranteed by the second law of thermodynamics. However, the interaction-induced coherence allows for positive work output under such conditions. Our model provides an autonomous implementation of Maxwell’s demon, where the measurement and feedback operations are driven by an adiabatically evolved Hamiltonian without external intervention. Furthermore, the coherence of the entire system is amplified by the heat reservoir after measurement, which is the key of the positive work output. Conversely, the quantum measurement-erase cycle typically outputs negative work, attributed to the decoherence of the instrument during the measurement process.

Maxwell's demon explores the role of information in physical processes.Employing information about microscopic degrees of freedom, this "intelligent observer" is capable of compensating entropy production (or extracting work), apparently challenging the second law of thermodynamics.In a modern standpoint, it is regarded as a feedback control mechanism and the limits of thermodynamics are recast incorporating information-to-energy conversion.We derive a trade-off relation between information-theoretic quantities empowering the design of an efficient Maxwell's demon in a quantum system.The demon is experimentally implemented as a spin-1=2 quantum memory that acquires information, and employs it to control the dynamics of another spin-1=2 system, through a natural interaction.Noise and imperfections in this protocol are investigated by the assessment of its effectiveness.This realization provides experimental evidence that the irreversibility in a nonequilibrium dynamics can be mitigated by assessing microscopic information and applying a feed-forward strategy at the quantum scale.

I study an autonomous quantum Maxwell's demon based on two exchange-coupled quantum dots attached to the spin-polarized leads. The principle of operation of the demon is based on the coherent oscillations between the spin states of the system which act as a quantum iSWAP gate. Due to the operation of the iSWAP gate, one of the dots acts as a feedback controller which blocks the transport with the bias in the other dot, thus inducing the electron pumping against the bias; this leads to the locally negative entropy production. Operation of the demon is associated with the information transfer between the dots, which is studied quantitatively by mapping the analyzed setup onto the thermodynamically equivalent auxiliary system. The calculated entropy production in a single subsystem and information flow between the subsystems are shown to obey a local form of the second law of thermodynamics, similar to the one previously derived for classical bipartite systems.

We study the modification of the second law of thermodynamics for a quantum system interacting with a reservoir regarding quantum coherence. The whole system is isolated so that neither energy nor information is lost. It is discovered that the coherence of the reservoir can serves as a useful resource allowing the system extract more energy from the reservoir; among the coherence measures, only is the relative entropy of coherence feasible to quantitatively characterize energy exchange. We demonstrate that a thermodynamic cycle between two coherent reservoirs can output more work than its classical counterpart. The efficiency of such cycle surpasses the Carnot efficiency, which is the upper bound of heat engine efficiency in classical regime.