arXiv:1602.04925 · Entropy

Quantum Heat Machines Equivalence, Work Extraction beyond Markovianity, and Strong Coupling via Heat Exchangers

Raam Uzdin, Amikam Levy, Ronnie Kosloff

Published Apr 6, 2016• 71 citations

Abstract

Various engine types are thermodynamically equivalent in the quantum limit of small “engine action”. Our previous derivation of the equivalence is restricted to Markovian heat baths and to implicit classical work repository (e.g., laser light in the semi-classical approximation). In this paper, all the components, baths, batteries, and engines, are explicitly taken into account. To neatly treat non-Markovian dynamics, we use mediating particles that function as a heat exchanger. We find that, on top of the previously observed equivalence, there is a higher degree of equivalence that cannot be achieved in the Markovian regime. Next, we focus on the quality of the battery charging process. A condition for positive energy increase and zero entropy increase (work) is given. Moreover, it is shown that, in the strong coupling regime, it is possible to super-charge a battery. With super-charging, the energy of the battery is increased while its entropy is being reduced at the same time.

DOI: 10.3390/e18040124

Related papers

Thermodynamics of Minimal Coupling Quantum Heat Engines

Marcin Łobejko, Paweł Mazurek, Michał Horodecki

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.

arXiv:2003.05788QuantumDec 23, 202025 citations

Surpassing the Carnot efficiency by extracting imperfect work

Nelly Huei Ying Ng, Mischa P. Woods, Stephanie Wehner

A suitable way of quantifying work for microscopic quantum systems has been constantly debated in the field of quantum thermodynamics. One natural approach is to measure the average increase in energy of an ancillary system, called the battery, after a work extraction protocol. The quality of energy extracted is usually argued to be good by quantifying higher moments of the energy distribution, or by restricting the amount of entropy to be low. This limits the amount of heat contribution to the energy extracted, but does not completely prevent it. We show that the definition of 'work' is crucial. If one allows for a definition of work that tolerates a non-negligible entropy increase in the battery, then a small scale heat engine can possibly exceed the Carnot efficiency. This can be done without using any additional resources such as coherence or correlations, and furthermore can be achieved even when one of the heat baths is finite in size.

arXiv:1606.05532New Journal of PhysicsSep 15, 201732 citations

Strong coupling non-Markovian quantum thermodynamics of a finite-bath system

Devvrat Tiwari, Baibhab Bose, Subhashish Banerjee

The focus is on understanding the quantum thermodynamics of strongly coupled non-Markovian quantum systems. To this end, a non-trivial, non-Markovian model of a central spin surrounded by a spin bath is taken up, and its exact evolution is derived for arbitrary system-bath couplings. The fundamental quantum thermodynamic quantities, such as system and bath internal energies, work, heat, entropy production, and ergotropy, are calculated using the dynamics and the original system (bath) Hamiltonian. An explicit expression for the work, a mismatch between the system and bath internal energies, is derived. The thermodynamic entropy of the system at thermal equilibrium is studied using the Hamiltonian of mean force in the strong coupling regime. The role of a canonical Hamiltonian in calculating the above thermodynamic quantities, a recently developed technique, is also investigated. Furthermore, an interesting observation relevant to the spin bath acting as a charger is made in a scenario where the central spin is envisaged as a quantum battery.

arXiv:2404.15915The Journal of Chemical PhysicsMar 17, 202515 citations

Switching the function of the quantum Otto cycle in non-Markovian dynamics: Heat engine, heater, and heat pump

Miku Ishizaki, Naomichi Hatano, Hiroyasu Tajima

Quantum thermodynamics explores novel thermodynamic phenomena that emerge when interactions between macroscopic systems and microscopic quantum ones go into action. Among various issues, quantum heat engines, in particular, have attracted much attention as a critical step in theoretical formulation of quantum thermodynamics and investigation of efficient use of heat by means of quantum resources. In the present paper, we focus on heat absorption and emission processes as well as work extraction processes of a quantum Otto cycle. We describe the former as non-Markovian dynamics, and thereby find that the interaction energy between a macroscopic heat bath and a microscopic qubit is not negligible. Specifically, we reveal that the interaction energy is divided into the system and the bath in a region of the short interaction time and remains negative in the region of the long interaction time. In addition, a counterintuitive energy flow from the system and the interaction energy to the hot bath occurs in another region of the short interaction time. We quantify these effects by defining an index of non-Markovianity in terms of the interaction energy. With this behavior of the interaction energy, we show that a non-Markovian quantum Otto cycle can switch functions such as an engine as well as a heater or a heat pump by controlling the interaction time with the heat bath. In particular, the qubit itself loses its energy if we shorten the interaction time, and in this sense, the qubit is cooled through the cycle. This property has a possibility of being utilized for cooling the qubits in quantum computing. We also describe the work extraction from the microscopic system to a macroscopic system like us humans as an indirect measurement process by introducing a work storage as a new reservoir.

arXiv:2211.09336Physical Review ResearchApr 27, 202321 citations

Measurement-based Formulation of Quantum Heat Engine and Optimal Efficiency with Finite-Size Effect

Hiroyasu Tajima, Masahito Hayashi

There exist two formulations for quantum heat engine. One is semi-classical scenario, and the other is full quantum scenario. The former is formulated as a unitary evolution for the internal system (working body and heat baths), and is adopted by the community of statistical mechanics. The latter is formulated as a unitary for the work storage and the internal system. It is adopted by the community of quantum information. However, these formulations do not consider measurement process. In this paper, we formulate the quantum heat engine based on the quantum measurement theory, because the amount of extracted work should be observed in a practical situation. With using our formulation, we derive two trade-off relations that show the semi-classical scenario does not work when the amount of extracted work is observed, i.e., we can hardly know the amount of the extracted work when the time evolution of the internal system is close to unitary. Next, based on our formulation, we derive the optimal efficiency of quantum heat engines with the finite-size heat baths, without assuming the existence of quasi-static processes. Using the strong large deviation theory, we asymptotically expand the optimal efficiency up to the third order. The first term is shown to be Carnot efficiency, and the higher order terms are shown to be the finite-size effects of the heat baths. We can construct the optimal work extraction as an energy-preserving unitary evolution among the internal system and the work storage. During the optimal work extraction, the entropy gain of the work storage is so negligibly small as compared with the energy gain of the work storage.

Apr 23, 20150 citations

Fundamental corrections to work and power in the strong coupling regime

Martí Perarnau-Llobet, Henrik Wilming, Arnau Riera +2 more

Quantum systems strongly coupled to many-body systems equilibrate to the reduced state of a global thermal state, deviating from the local thermal state of the system as it occurs in the weak-coupling limit. Taking this insight as a starting point, we study the thermodynamics of systems strongly coupled to thermal baths. First, we provide strong-coupling corrections to the second law applicable to general systems in three of its different readings: As a statement of maximal extractable work, on heat dissipation, and bound to the Carnot efficiency. These corrections become relevant for small quantum systems and always vanish in first order in the interaction strength. We then move to the question of power of heat engines, obtaining a bound on the power enhancement due to strong coupling. Our results are exemplified on the paradigmatic situation of non-Markovian quantum Brownian motion.

Apr 19, 20174 citations