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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: closed (30 July 2017) | Viewed by 167642

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Special Issue Editor

Prof. Dr. Ronnie Kosloff

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Guest Editor

Institute of Chemistry, Hebrew University, Jerusalem 91904, Israel
Interests: quantum thermodynamics; quantum heat engines; quantum refrigerators; quantum dynamics; quantum control; quantum information
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Quantum thermodynamics is the study of the relations between two independent physical theories: thermodynamics and quantum mechanics. Both theories address the same physical phenomena of light and matter. In 1905, Einstein postulated that the requirement of consistency between thermodynamics and electromagnetism leads to the conclusion that light is quantized.

Currently, quantum thermodynamics addresses the emergence of thermodynamic phenomena from quantum mechanics. In addition, to what extent do the paradigms of thermodynamics apply in the quantum domain, when quantum effects, such as quantum correlation, quantum fluctuation, coherences and entanglement, come into play. Emerging novel quantum technology motivates the quest for smaller devices. Such devices operating at the quantum level form the foundation for quantum information and quantum metrology. These devices have to be cooled, requiring quantum refrigerators. Any practical consideration will therefore involve thermodynamical principles.

The field of quantum thermodynamics is going through rapid development with contributions from many fields of science physics, such as open quantum systems, quantum information, quantum optics, statistical physics, solid state, cold atoms, optomechanics and more. This interdisciplinary character leads to different viewpoints. I, therefore, solicit contribution to this Special Issue of the many faces of quantum thermodynamics.

Prof. Dr. Ronnie Kosloff
Guest Editor

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Keywords

The emergence of thermodynamics from quantum mechanics.
Thermalization of quantum systems.
Quantum signatures in thermodynamics.
Manifestations of quantum phenomena in thermodynamics.
Quantum heat transport.
Quantum heat engines and refrigerators.
Quantum thermodynamic resource theory.
Experimental realization of quantum thermodynamic effects.
Quantum fluctuation relations.

Related Special Issues

Thermodynamics of Quantum Information in Entropy (6 articles)
Quantum Thermodynamics II in Entropy (8 articles)

Published Papers (22 papers)

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322 KiB

Open AccessArticle

The Isolated Electron: De Broglie’s Hidden Thermodynamics, SU(2) Quantum Yang-Mills Theory, and a Strongly Perturbed BPS Monopole

by Ralf Hofmann

Entropy 2017, 19(11), 575; https://0-doi-org.brum.beds.ac.uk/10.3390/e19110575 - 26 Oct 2017

Cited by 6 | Viewed by 9640

Abstract

Based on a recent numerical simulation of the temporal evolution of a spherically perturbed BPS monopole, SU(2) Yang-Mills thermodynamics, Louis de Broglie’s deliberations on the disparate Lorentz transformations of the frequency of an internal “clock” on one hand and the associated quantum energy on the other hand, and postulating that the electron is represented by a figure-eight shaped, self-intersecting center vortex loop in SU(2) Quantum Yang-Mills theory we estimate the spatial radius

R_{0}

of this self-intersection region in terms of the electron’s Compton wave length

λ_{C}

. This region, which is immersed into the confining phase, constitutes a blob of deconfining phase of temperature

T_{0}

mildly above the critical temperature

T_{c}

carrying a frequently perturbed BPS monopole (with a magnetic-electric dual interpretation of its charge w.r.t. U(1)⊂SU(2)). We also establish a quantitative relation between rest mass

m_{0}

of the electron and SU(2) Yang-Mills scale

Λ

, which in turn is defined via

T_{c}

. Surprisingly,

R_{0}

turns out to be comparable to the Bohr radius while the core size of the monopole matches

λ_{C}

, and the correction to the mass of the electron due to Coulomb energy is about 2%. Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

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490 KiB

Open AccessArticle

Implications of Coupling in Quantum Thermodynamic Machines

by George Thomas, Manik Banik and Sibasish Ghosh

Entropy 2017, 19(9), 442; https://0-doi-org.brum.beds.ac.uk/10.3390/e19090442 - 08 Sep 2017

Cited by 18 | Viewed by 5692

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. Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

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973 KiB

Open AccessArticle

Molecular Heat Engines: Quantum Coherence Effects

by Feng Chen, Yi Gao and Michael Galperin

Entropy 2017, 19(9), 472; https://0-doi-org.brum.beds.ac.uk/10.3390/e19090472 - 04 Sep 2017

Cited by 20 | Viewed by 5585

Abstract

Recent developments in nanoscale experimental techniques made it possible to utilize single molecule junctions as devices for electronics and energy transfer with quantum coherence playing an important role in their thermoelectric characteristics. Theoretical studies on the efficiency of nanoscale devices usually employ rate (Pauli) equations, which do not account for quantum coherence. Therefore, the question whether quantum coherence could improve the efficiency of a molecular device cannot be fully addressed within such considerations. Here, we employ a nonequilibrium Green function approach to study the effects of quantum coherence and dephasing on the thermoelectric performance of molecular heat engines. Within a generic bichromophoric donor-bridge-acceptor junction model, we show that quantum coherence may increase efficiency compared to quasi-classical (rate equation) predictions and that pure dephasing and dissipation destroy this effect. Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

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322 KiB

Open AccessArticle

Deformed Jarzynski Equality

by Jiawen Deng, Juan D. Jaramillo, Peter Hänggi and Jiangbin Gong

Entropy 2017, 19(8), 419; https://0-doi-org.brum.beds.ac.uk/10.3390/e19080419 - 18 Aug 2017

Cited by 6 | Viewed by 5331

Abstract

The well-known Jarzynski equality, often written in the form

e^{- β Δ F} = ⟨ e^{- β W} ⟩

, provides a non-equilibrium means to measure the free energy difference

Δ F

of a system at the same inverse temperature [...] Read more.

The well-known Jarzynski equality, often written in the form

e^{- β Δ F} = 〈 e^{- β W} 〉

, provides a non-equilibrium means to measure the free energy difference

Δ F

of a system at the same inverse temperature

β

based on an ensemble average of non-equilibrium work W. The accuracy of Jarzynski’s measurement scheme was known to be determined by the variance of exponential work, denoted as

var (e^{- β W})

. However, it was recently found that

var (e^{- β W})

can systematically diverge in both classical and quantum cases. Such divergence will necessarily pose a challenge in the applications of Jarzynski equality because it may dramatically reduce the efficiency in determining

Δ F

. In this work, we present a deformed Jarzynski equality for both classical and quantum non-equilibrium statistics, in efforts to reuse experimental data that already suffers from a diverging

var (e^{- β W})

. The main feature of our deformed Jarzynski equality is that it connects free energies at different temperatures and it may still work efficiently subject to a diverging

var (e^{- β W})

. The conditions for applying our deformed Jarzynski equality may be met in experimental and computational situations. If so, then there is no need to redesign experimental or simulation methods. Furthermore, using the deformed Jarzynski equality, we exemplify the distinct behaviors of classical and quantum work fluctuations for the case of a time-dependent driven harmonic oscillator dynamics and provide insights into the essential performance differences between classical and quantum Jarzynski equalities. Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

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249 KiB

Open AccessArticle

Axiomatic Characterization of the Quantum Relative Entropy and Free Energy

by Henrik Wilming, Rodrigo Gallego and Jens Eisert

Entropy 2017, 19(6), 241; https://0-doi-org.brum.beds.ac.uk/10.3390/e19060241 - 23 May 2017

Cited by 27 | Viewed by 5750

Abstract

Building upon work by Matsumoto, we show that the quantum relative entropy with full-rank second argument is determined by four simple axioms: (i) Continuity in the first argument; (ii) the validity of the data-processing inequality; (iii) additivity under tensor products; and (iv) super-additivity. This observation has immediate implications for quantum thermodynamics, which we discuss. Specifically, we demonstrate that, under reasonable restrictions, the free energy is singled out as a measure of athermality. In particular, we consider an extended class of Gibbs-preserving maps as free operations in a resource-theoretic framework, in which a catalyst is allowed to build up correlations with the system at hand. The free energy is the only extensive and continuous function that is monotonic under such free operations. Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

406 KiB

Open AccessArticle

Kinetics of Interactions of Matter, Antimatter and Radiation Consistent with Antisymmetric (CPT-Invariant) Thermodynamics

by A.Y. Klimenko

Entropy 2017, 19(5), 202; https://0-doi-org.brum.beds.ac.uk/10.3390/e19050202 - 02 May 2017

Cited by 3 | Viewed by 4560

Abstract

This work investigates the influence of directional properties of decoherence on kinetics rate equations. The physical reality is understood as a chain of unitary and decoherence events. The former are quantum-deterministic, while the latter introduce uncertainty and increase entropy. For interactions of matter and antimatter, two approaches are considered: symmetric decoherence, which corresponds to conventional symmetric (CP-invariant) thermodynamics, and antisymmetric decoherence, which corresponds to antisymmetric (CPT-invariant) thermodynamics. Radiation, in its interactions with matter and antimatter, is shown to be decoherence-neutral. The symmetric and antisymmetric assumptions result in different interactions of radiation with matter and antimatter. The theoretical predictions for these differences are testable by comparing absorption (emission) of light by thermodynamic systems made of matter and antimatter. Canonical typicality for quantum mixtures is briefly discussed in Appendix A. Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

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Open AccessArticle

Nonequilibrium Thermodynamics and Steady State Density Matrix for Quantum Open Systems

by Hervé Ness

Entropy 2017, 19(4), 158; https://0-doi-org.brum.beds.ac.uk/10.3390/e19040158 - 02 Apr 2017

Cited by 15 | Viewed by 6078

Abstract

We consider the generic model of a finite-size quantum electron system connected to two (temperature and particle) reservoirs. The quantum open system is driven out of equilibrium by the presence of both potential temperature and chemical differences between the two reservoirs. The nonequilibrium (NE) thermodynamical properties of such a quantum open system are studied for the steady state regime. In such a regime, the corresponding NE density matrix is built on the so-called generalised Gibbs ensembles. From different expressions of the NE density matrix, we can identify the terms related to the entropy production in the system. We show, for a simple model, that the entropy production rate is always a positive quantity. Alternative expressions for the entropy production are also obtained from the Gibbs–von Neumann conventional formula and discussed in detail. Our results corroborate and expand earlier works found in the literature. Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

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488 KiB

Open AccessArticle

Quantum Thermodynamics with Degenerate Eigenstate Coherences

by Gregory Bulnes Cuetara, Massimiliano Esposito and Gernot Schaller

Entropy 2016, 18(12), 447; https://0-doi-org.brum.beds.ac.uk/10.3390/e18120447 - 15 Dec 2016

Cited by 33 | Viewed by 8396

Abstract

We establish quantum thermodynamics for open quantum systems weakly coupled to their reservoirs when the system exhibits degeneracies. The first and second law of thermodynamics are derived, as well as a finite-time fluctuation theorem for mechanical work and energy and matter currents. Using a double quantum dot junction model, local eigenbasis coherences are shown to play a crucial role on thermodynamics and on the electron counting statistics. Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

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306 KiB

Open AccessArticle

SU(2) Yang–Mills Theory: Waves, Particles, and Quantum Thermodynamics

by Ralf Hofmann

Entropy 2016, 18(9), 310; https://0-doi-org.brum.beds.ac.uk/10.3390/e18090310 - 23 Aug 2016

Cited by 11 | Viewed by 16694

Abstract

We elucidate how Quantum Thermodynamics at temperature T emerges from pure and classical

S U (2)

Yang–Mills theory on a four-dimensional Euclidean spacetime slice

S_{1} \times R^{3}

. The concept of a (deconfining) thermal ground state, composed of certain [...] Read more.

We elucidate how Quantum Thermodynamics at temperature T emerges from pure and classical

S U (2)

Yang–Mills theory on a four-dimensional Euclidean spacetime slice

S_{1} \times R^{3}

. The concept of a (deconfining) thermal ground state, composed of certain solutions to the fundamental, classical Yang–Mills equation, allows for a unified addressation of both (classical) wave- and (quantum) particle-like excitations thereof. More definitely, the thermal ground state represents the interplay between nonpropagating, periodic configurations which are electric-magnetically (anti)selfdual in a non-trivial way and possess topological charge modulus unity. Their trivial-holonomy versions—Harrington–Shepard (HS) (anti)calorons—yield an accurate a priori estimate of the thermal ground state in terms of spatially coarse-grained centers, each containing one quantum of action ℏ localized at its inmost spacetime point, which induce an inert adjoint scalar field

ϕ

(

| ϕ |

spatio-temporally constant). The field

ϕ

, in turn, implies an effective pure-gauge configuration,

a_{μ}^{gs}

, accurately describing HS (anti)caloron overlap. Spatial homogeneity of the thermal ground-state estimate

ϕ, a_{μ}^{gs}

demands that (anti)caloron centers are densely packed, thus representing a collective departure from (anti)selfduality. Effectively, such a “nervous” microscopic situation gives rise to two static phenomena: finite ground-state energy density

ρ_{gs}

and pressure

P_{gs}

with

ρ_{gs} = - P_{gs}

as well as the (adjoint) Higgs mechanism. The peripheries of HS (anti)calorons are static and resemble (anti)selfdual dipole fields whose apparent dipole moments are determined by

| ϕ |

and T, protecting them against deformation potentially caused by overlap. Such a protection extends to the spatial density of HS (anti)caloron centers. Thus the vacuum electric permittivity

ϵ_{0}

and magnetic permeability

μ_{0}

, supporting the propagation of wave-like disturbances in the

U (1)

Cartan subalgebra of

S U (2)

, can be reliably calculated for disturbances which do not probe HS (anti)caloron centers. Both

ϵ_{0}

and

μ_{0}

turn out to be temperature independent in thermal equilibrium but also for an isolated, monochromatic

U (1)

wave. HS (anti)caloron centers, on the other hand, react onto wave-like disturbances, which would resolve their spatio-temporal structure, by indeterministic emissions of quanta of energy and momentum. Thermodynamically seen, such events are Boltzmann weighted and occur independently at distinct locations in space and instants in (Minkowskian) time, entailing the Bose–Einstein distribution. Small correlative ramifications associate with effective radiative corrections, e.g., in terms of polarization tensors. We comment on an

S U (2)

S U (2)

based gauge-theory model, describing wave- and particle-like aspects of electromagnetic disturbances within the so far experimentally/observationally investigated spectrum. Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

1147 KiB

Open AccessArticle

Multiatom Quantum Coherences in Micromasers as Fuel for Thermal and Nonthermal Machines

by Ceren B. Dağ, Wolfgang Niedenzu, Özgür E. Müstecaplıoğlu and Gershon Kurizki

Entropy 2016, 18(7), 244; https://0-doi-org.brum.beds.ac.uk/10.3390/e18070244 - 29 Jun 2016

Cited by 81 | Viewed by 8380

Abstract

In this paper, we address the question: To what extent is the quantum state preparation of multiatom clusters (before they are injected into the microwave cavity) instrumental for determining not only the kind of machine we may operate, but also the quantitative bounds of its performance? Figuratively speaking, if the multiatom cluster is the “crude oil”, the question is: Which preparation of the cluster is the refining process that can deliver a “gasoline” with a “specific octane”? We classify coherences or quantum correlations among the atoms according to their ability to serve as: (i) fuel for nonthermal machines corresponding to atomic states whose coherences displace or squeeze the cavity field, as well as cause its heating; and (ii) fuel that is purely “combustible”, i.e., corresponds to atomic states that only allow for heat and entropy exchange with the field and can energize a proper heat engine. We identify highly promising multiatom states for each kind of fuel and propose viable experimental schemes for their implementation. Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

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337 KiB

Open AccessArticle

Unified Quantum Model of Work Generation in Thermoelectric Generators, Solar and Fuel Cells

by Robert Alicki

Entropy 2016, 18(6), 210; https://0-doi-org.brum.beds.ac.uk/10.3390/e18060210 - 28 May 2016

Cited by 12 | Viewed by 5546

Abstract

In the previous papers, the idea of “hidden oscillations” has been applied to explain work generation in semiconductor photovoltaic cells and thermoelectric generators. The aim of this paper is firstly to extend this approach to fuel cells and, secondly, to create a unified quantum model for all types of such devices. They are treated as electron pumps powered by heat or chemical engines. The working fluid is electron gas and the necessary oscillating element (“piston”) is provided by plasma oscillation. Those oscillations are localized around the junction that also serves as a diode rectifying fast electric charge oscillations and yielding a final output direct current (DC). The dynamics of the devices are governed by the Markovian master equations that can be derived in a rigorous way from the underlying Hamiltonian models and are consistent with the laws of thermodynamics. The new ingredient is the derivation of master equations for systems driven by chemical reactions. Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

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488 KiB

Open AccessArticle

Quantum Coherent Three-Terminal Thermoelectrics: Maximum Efficiency at Given Power Output

by Robert S. Whitney

Entropy 2016, 18(6), 208; https://0-doi-org.brum.beds.ac.uk/10.3390/e18060208 - 27 May 2016

Cited by 19 | Viewed by 5057

Abstract

This work considers the nonlinear scattering theory for three-terminal thermoelectric devices used for power generation or refrigeration. Such systems are quantum phase-coherent versions of a thermocouple, and the theory applies to systems in which interactions can be treated at a mean-field level. It considers an arbitrary three-terminal system in any external magnetic field, including systems with broken time-reversal symmetry, such as chiral thermoelectrics, as well as systems in which the magnetic field plays no role. It is shown that the upper bound on efficiency at given power output is of quantum origin and is stricter than Carnot’s bound. The bound is exactly the same as previously found for two-terminal devices and can be achieved by three-terminal systems with or without broken time-reversal symmetry, i.e., chiral and non-chiral thermoelectrics. Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

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984 KiB

Open AccessArticle

Quantum Thermodynamics in Strong Coupling: Heat Transport and Refrigeration

by Gil Katz and Ronnie Kosloff

Entropy 2016, 18(5), 186; https://0-doi-org.brum.beds.ac.uk/10.3390/e18050186 - 16 May 2016

Cited by 59 | Viewed by 8854

Abstract

The performance characteristics of a heat rectifier and a heat pump are studied in a non-Markovian framework. The device is constructed from a molecule connected to a hot and cold reservoir. The heat baths are modelled using the stochastic surrogate Hamiltonian method. The molecule is modelled by an asymmetric double-well potential. Each well is semi-locally connected to a heat bath composed of spins. The dynamics are driven by a combined system–bath Hamiltonian. The temperature of the baths is regulated by a secondary spin bath composed of identical spins in thermal equilibrium. A random swap operation exchange spins between the primary and secondary baths. The combined system is studied in various system–bath coupling strengths. In all cases, the average heat current always flows from the hot towards the cold bath in accordance with the second law of thermodynamics. The asymmetry of the double well generates a rectifying effect, meaning that when the left and right baths are exchanged the heat current follows the hot-to-cold direction. The heat current is larger when the high frequency is coupled to the hot bath. Adding an external driving field can reverse the transport direction. Such a refrigeration effect is modelled by a periodic driving field in resonance with the frequency difference of the two potential wells. A minimal driving amplitude is required to overcome the heat leak effect. In the strong driving regime the cooling power is non-monotonic with the system–bath coupling. Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

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898 KiB

Open AccessArticle

Magnetically-Driven Quantum Heat Engines: The Quasi-Static Limit of Their Efficiency

by Enrique Muñoz, Francisco J. Peña and Alejandro González

Entropy 2016, 18(5), 173; https://0-doi-org.brum.beds.ac.uk/10.3390/e18050173 - 06 May 2016

Cited by 13 | Viewed by 8780

Abstract

The concept of a quantum heat engine (QHEN) has been discussed in the literature, not only due to its intrinsic scientific interest, but also as an alternative to efficiently recover, on a nanoscale device, thermal energy in the form of useful work. The quantum character of a QHEN relies, for instance, on the fact that any of its intermediate states is determined by a density matrix operator. In particular, this matrix can represent a mixed state. For a classical heat engine, a theoretical upper bound for its efficiency is obtained by analyzing its quasi-static operation along a cycle drawn by a sequence of quasi-equilibrium states. A similar analysis can be carried out for a quantum engine, where quasi-static processes are driven by the evolution of ensemble-averaged observables, via variation of the corresponding operators or of the density matrix itself on a tunable physical parameter. We recently proposed two new conceptual designs for a magnetically-driven quantum engine, where the tunable parameter is the intensity of an external magnetic field. Along this article, we shall present the general quantum thermodynamics formalism developed in order to analyze this type of QHEN, and moreover, we shall apply it to describe the theoretical efficiency of two different practical implementations of this concept: an array of semiconductor quantum dots and an ensemble of graphene flakes submitted to mechanical tension. Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

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497 KiB

Open AccessFeature PaperArticle

Scaling-Up Quantum Heat Engines Efficiently via Shortcuts to Adiabaticity

by Mathieu Beau, Juan Jaramillo and Adolfo Del Campo

Entropy 2016, 18(5), 168; https://0-doi-org.brum.beds.ac.uk/10.3390/e18050168 - 30 Apr 2016

Cited by 120 | Viewed by 9485

Abstract

The finite-time operation of a quantum heat engine that uses a single particle as a working medium generally increases the output power at the expense of inducing friction that lowers the cycle efficiency. We propose to scale up a quantum heat engine utilizing a many-particle working medium in combination with the use of shortcuts to adiabaticity to boost the nonadiabatic performance by eliminating quantum friction and reducing the cycle time. To this end, we first analyze the finite-time thermodynamics of a quantum Otto cycle implemented with a quantum fluid confined in a time-dependent harmonic trap. We show that nonadiabatic effects can be controlled and tailored to match the adiabatic performance using a variety of shortcuts to adiabaticity. As a result, the nonadiabatic dynamics of the scaled-up many-particle quantum heat engine exhibits no friction, and the cycle can be run at maximum efficiency with a tunable output power. We demonstrate our results with a working medium consisting of particles with inverse-square pairwise interactions that includes non-interacting and hard-core bosons as limiting cases. Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

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493 KiB

Open AccessArticle

Performance of Continuous Quantum Thermal Devices Indirectly Connected to Environments

by J. Onam González, Daniel Alonso and José P. Palao

Entropy 2016, 18(5), 166; https://0-doi-org.brum.beds.ac.uk/10.3390/e18050166 - 28 Apr 2016

Cited by 4 | Viewed by 4557

Abstract

A general quantum thermodynamics network is composed of thermal devices connected to environments through quantum wires. The coupling between the devices and the wires may introduce additional decay channels which modify the system performance with respect to the directly-coupled device. We analyze this effect in a quantum three-level device connected to a heat bath or to a work source through a two-level wire. The steady state heat currents are decomposed into the contributions of the set of simple circuits in the graph representing the master equation. Each circuit is associated with a mechanism in the device operation and the system performance can be described by a small number of circuit representatives of those mechanisms. Although in the limit of weak coupling between the device and the wire the new irreversible contributions can become small, they prevent the system from reaching the Carnot efficiency. Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

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411 KiB

Open AccessArticle

Testing a Quantum Heat Pump with a Two-Level Spin

by Luis A. Correa and Mohammad Mehboudi

Entropy 2016, 18(4), 141; https://0-doi-org.brum.beds.ac.uk/10.3390/e18040141 - 15 Apr 2016

Cited by 6 | Viewed by 5656

Abstract

Once in its non-equilibrium steady state, a nanoscale system coupled to several heat baths may be thought of as a “quantum heat pump”. Depending on the direction of its stationary heat flows, it may function as, e.g., a refrigerator or a heat transformer. These continuous heat devices can be arbitrarily complex multipartite systems, and yet, their working principle is always the same: they are made up of several elementary three-level stages operating in parallel. As a result, it is possible to devise external “black-box” testing strategies to learn about their functionality and performance regardless of any internal details. In particular, one such heat pump can be tested by coupling a two-level spin to one of its “contact transitions”. The steady state of this external probe contains information about the presence of heat leaks and internal dissipation in the device and, also, about the direction of its steady-state heat currents. Provided that the irreversibility of the heat pump is low, one can further estimate its coefficient of performance. These techniques may find applications in the emerging field of quantum thermal engineering, as they facilitate the diagnosis and design optimization of complex thermodynamic cycles. Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

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783 KiB

Open AccessArticle

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

by Raam Uzdin, Amikam Levy and Ronnie Kosloff

Entropy 2016, 18(4), 124; https://0-doi-org.brum.beds.ac.uk/10.3390/e18040124 - 06 Apr 2016

Cited by 58 | Viewed by 9133

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. Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

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1130 KiB

Open AccessArticle

Thermodynamics of Quantum Feedback Cooling

by Pietro Liuzzo-Scorpo, Luis A. Correa, Rebecca Schmidt and Gerardo Adesso

Entropy 2016, 18(2), 48; https://0-doi-org.brum.beds.ac.uk/10.3390/e18020048 - 04 Feb 2016

Cited by 23 | Viewed by 6591

Abstract

The ability to initialize quantum registers in pure states lies at the core of many applications of quantum technologies, from sensing to quantum information processing and computation. In this paper, we tackle the problem of increasing the polarization bias of an ensemble of two-level register spins by means of joint coherent manipulations, involving a second ensemble of ancillary spins and energy dissipation into an external heat bath. We formulate this spin refrigeration protocol, akin to algorithmic cooling, in the general language of quantum feedback control, and identify the relevant thermodynamic variables involved. Our analysis is two-fold: on the one hand, we assess the optimality of the protocol by means of suitable figures of merit, accounting for both its work cost and effectiveness; on the other hand, we characterise the nature of correlations built up between the register and the ancilla. In particular, we observe that neither the amount of classical correlations nor the quantum entanglement seem to be key ingredients fuelling our spin refrigeration protocol. We report instead that a more general indicator of quantumness beyond entanglement, the so-called quantum discord, is closely related to the cooling performance. Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

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Open AccessArticle

Schroedinger vs. Navier–Stokes

by P. Fernández de Córdoba, J. M. Isidro and J. Vázquez Molina

Entropy 2016, 18(1), 34; https://0-doi-org.brum.beds.ac.uk/10.3390/e18010034 - 19 Jan 2016

Cited by 6 | Viewed by 5647

Abstract

Quantum mechanics has been argued to be a coarse-graining of some underlying deterministic theory. Here we support this view by establishing a map between certain solutions of the Schroedinger equation, and the corresponding solutions of the irrotational Navier–Stokes equation for viscous fluid flow. As a physical model for the fluid itself we propose the quantum probability fluid. It turns out that the (state-dependent) viscosity of this fluid is proportional to Planck’s constant, while the volume density of entropy is proportional to Boltzmann’s constant. Stationary states have zero viscosity and a vanishing time rate of entropy density. On the other hand, the nonzero viscosity of nonstationary states provides an information-loss mechanism whereby a deterministic theory (a classical fluid governed by the Navier–Stokes equation) gives rise to an emergent theory (a quantum particle governed by the Schroedinger equation). Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

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The Quantum Harmonic Otto Cycle

by Ronnie Kosloff and Yair Rezek

Entropy 2017, 19(4), 136; https://0-doi-org.brum.beds.ac.uk/10.3390/e19040136 - 23 Mar 2017

Cited by 268 | Viewed by 14391

Abstract

The quantum Otto cycle serves as a bridge between the macroscopic world of heat engines and the quantum regime of thermal devices composed from a single element. We compile recent studies of the quantum Otto cycle with a harmonic oscillator as a working medium. This model has the advantage that it is analytically trackable. In addition, an experimental realization has been achieved, employing a single ion in a harmonic trap. The review is embedded in the field of quantum thermodynamics and quantum open systems. The basic principles of the theory are explained by a specific example illuminating the basic definitions of work and heat. The relation between quantum observables and the state of the system is emphasized. The dynamical description of the cycle is based on a completely positive map formulated as a propagator for each stroke of the engine. Explicit solutions for these propagators are described on a vector space of quantum thermodynamical observables. These solutions which employ different assumptions and techniques are compared. The tradeoff between power and efficiency is the focal point of finite-time-thermodynamics. The dynamical model enables the study of finite time cycles limiting time on the adiabatic and the thermalization times. Explicit finite time solutions are found which are frictionless (meaning that no coherence is generated), and are also known as shortcuts to adiabaticity.The transition from frictionless to sudden adiabats is characterized by a non-hermitian degeneracy in the propagator. In addition, the influence of noise on the control is illustrated. These results are used to close the cycles either as engines or as refrigerators. The properties of the limit cycle are described. Methods to optimize the power by controlling the thermalization time are also introduced. At high temperatures, the Novikov–Curzon–Ahlborn efficiency at maximum power is obtained. The sudden limit of the engine which allows finite power at zero cycle time is shown. The refrigerator cycle is described within the frictionless limit, with emphasis on the cooling rate when the cold bath temperature approaches zero. Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

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Open AccessReview

Periodic Energy Transport and Entropy Production in Quantum Electronics

by María Florencia Ludovico, Liliana Arrachea, Michael Moskalets and David Sánchez

Entropy 2016, 18(11), 419; https://0-doi-org.brum.beds.ac.uk/10.3390/e18110419 - 23 Nov 2016

Cited by 47 | Viewed by 6021

Abstract

The problem of time-dependent particle transport in quantum conductors is nowadays a well established topic. In contrast, the way in which energy and heat flow in mesoscopic systems subjected to dynamical drivings is a relatively new subject that cross-fertilize both fundamental developments of quantum thermodynamics and practical applications in nanoelectronics and quantum information. In this short review, we discuss from a thermodynamical perspective recent investigations on nonstationary heat and work generated in quantum systems, emphasizing open questions and unsolved issues. Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

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