Special Issue "Fluctuation Relations and Nonequilibrium Thermodynamics in Classical and Quantum Systems"

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (31 December 2019).

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Dr. Gabriele De Chiara
E-Mail Website
Guest Editor
Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast, BT7 1NN, UK
Interests: quantum technologies; correlations and out-of-equilibrium thermodynamics of many-body systems

Special Issue Information

Dear Colleagues,

The recent advances in the control of microscopic systems down to the atomic level have triggered a renewed interest in the study of the thermodynamic processes of small systems. As these are characterised by strong fluctuations of thermal and quantum origins, thermodynamic quantities like heat, work, and entropy become stochastic variables. Fluctuation theorems, including the most celebrated Jarzynski relation, connect exponential averages of these quantities, even for out-of-equilibrium processes, with equilibrium observables like free energy differences.

On the one hand, in the classical stochastic thermodynamic setting, fluctuation theorems are well established and experimentally verified under appropriate conditions (e.g., initial equilibrium and weak coupling). However, in recent years, these assumptions have been challenged and new fluctuations have been discovered. On the other hand, fluctuation theorems in the quantum domain have been studied quite recently. According to the so-called two-time measurement definition of work, the quantum Jarzynski relation has been verified in experiments with nuclear magnetic resonance and trapped ion setups. However, the very definition of work is still under active debate, since it is known that the two-time measurement protocol leads to inconsistencies with the laws of thermodynamics. Moreover, for open quantum systems, approaches based on quantum trajectories have been put forward in the last few years.

Further recent investigations include the design and realisation of quantum thermal engines and refrigerators with the ambitious goal of understanding whether a quantum advantage, due to genuine quantum correlations or coherence, is possible in such devices. Insights from quantum information theory are helping to formalise quantum thermodynamics as a resource theory.

The areas covered in this Special Issue include but are not restricted to:

*) Fluctuation relations in classical stochastic thermodynamics

*) Definitions of work, heat, and entropy and related fluctuation theorems in quantum systems

*) Quantum engines and refrigerators

*) Resource theory of quantum thermodynamics

*) Role of quantum correlations and coherence in quantum thermodynamics

Dr. Gabriele De Chiara
Guest Editor

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Keywords

  • quantum thermodynamics
  • out-of-equilibrium thermodynamics
  • fluctuation theorems
  • work, heat, and entropy
  • quantum engines
  • open quantum systems
  • quantum resource theories

Published Papers (9 papers)

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Research

Open AccessArticle
Joint Fluctuation Theorems for Sequential Heat Exchange
Entropy 2020, 22(7), 763; https://doi.org/10.3390/e22070763 - 12 Jul 2020
Cited by 2 | Viewed by 805
Abstract
We study the statistics of heat exchange of a quantum system that collides sequentially with an arbitrary number of ancillas. This can describe, for instance, an accelerated particle going through a bubble chamber. Unlike other approaches in the literature, our focus is on [...] Read more.
We study the statistics of heat exchange of a quantum system that collides sequentially with an arbitrary number of ancillas. This can describe, for instance, an accelerated particle going through a bubble chamber. Unlike other approaches in the literature, our focus is on the joint probability distribution that heat Q 1 is exchanged with ancilla 1, heat Q 2 is exchanged with ancilla 2, and so on. This allows us to address questions concerning the correlations between the collisional events. For instance, if in a given realization a large amount of heat is exchanged with the first ancilla, then there is a natural tendency for the second exchange to be smaller. The joint distribution is found to satisfy a Fluctuation theorem of the Jarzynski–Wójcik type. Rather surprisingly, this fluctuation theorem links the statistics of multiple collisions with that of independent single collisions, even though the heat exchanges are statistically correlated. Full article
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Open AccessArticle
A Quantum Heat Exchanger for Nanotechnology
Entropy 2020, 22(4), 379; https://doi.org/10.3390/e22040379 - 26 Mar 2020
Viewed by 1260
Abstract
In this paper, we design a quantum heat exchanger which converts heat into light on relatively short quantum optical time scales. Our scheme takes advantage of heat transfer as well as collective cavity-mediated laser cooling of an atomic gas inside a cavitating bubble. [...] Read more.
In this paper, we design a quantum heat exchanger which converts heat into light on relatively short quantum optical time scales. Our scheme takes advantage of heat transfer as well as collective cavity-mediated laser cooling of an atomic gas inside a cavitating bubble. Laser cooling routinely transfers individually trapped ions to nano-Kelvin temperatures for applications in quantum technology. The quantum heat exchanger which we propose here might be able to provide cooling rates of the order of Kelvin temperatures per millisecond and is expected to find applications in micro- and nanotechnology. Full article
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Open AccessEditor’s ChoiceArticle
Quantifying Athermality and Quantum Induced Deviations from Classical Fluctuation Relations
Entropy 2020, 22(1), 111; https://doi.org/10.3390/e22010111 - 16 Jan 2020
Viewed by 1315
Abstract
In recent years, a quantum information theoretic framework has emerged for incorporating non-classical phenomena into fluctuation relations. Here, we elucidate this framework by exploring deviations from classical fluctuation relations resulting from the athermality of the initial thermal system and quantum coherence of the [...] Read more.
In recent years, a quantum information theoretic framework has emerged for incorporating non-classical phenomena into fluctuation relations. Here, we elucidate this framework by exploring deviations from classical fluctuation relations resulting from the athermality of the initial thermal system and quantum coherence of the system’s energy supply. In particular, we develop Crooks-like equalities for an oscillator system which is prepared either in photon added or photon subtracted thermal states and derive a Jarzynski-like equality for average work extraction. We use these equalities to discuss the extent to which adding or subtracting a photon increases the informational content of a state, thereby amplifying the suppression of free energy increasing process. We go on to derive a Crooks-like equality for an energy supply that is prepared in a pure binomial state, leading to a non-trivial contribution from energy and coherence on the resultant irreversibility. We show how the binomial state equality fits in relation to a previously derived coherent state equality and offers a richer feature-set. Full article
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Open AccessArticle
Thermalization of Finite Many-Body Systems by a Collision Model
Entropy 2019, 21(12), 1182; https://doi.org/10.3390/e21121182 - 30 Nov 2019
Cited by 4 | Viewed by 2006
Abstract
We construct a collision model description of the thermalization of a finite many-body system by using careful derivation of the corresponding Lindblad-type master equation in the weak coupling regime. Using the example of a two-level target system, we show that collision model thermalization [...] Read more.
We construct a collision model description of the thermalization of a finite many-body system by using careful derivation of the corresponding Lindblad-type master equation in the weak coupling regime. Using the example of a two-level target system, we show that collision model thermalization is crucially dependent on the various relevant system and bath timescales and on ensuring that the environment is composed of ancillae which are resonant with the system transition frequencies. Using this, we extend our analysis to show that our collision model can lead to thermalization for certain classes of many-body systems. We establish that for classically correlated systems our approach is effective, while we also highlight its shortcomings, in particular with regards to reaching entangled thermal states. Full article
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Open AccessArticle
Daemonic Ergotropy: Generalised Measurements and Multipartite Settings
Entropy 2019, 21(8), 771; https://doi.org/10.3390/e21080771 - 07 Aug 2019
Cited by 4 | Viewed by 1289
Abstract
Recently, the concept of daemonic ergotropy has been introduced to quantify the maximum energy that can be obtained from a quantum system through an ancilla-assisted work extraction protocol based on information gain via projective measurements [G. Francica et al., npj Quant. Inf. 3 [...] Read more.
Recently, the concept of daemonic ergotropy has been introduced to quantify the maximum energy that can be obtained from a quantum system through an ancilla-assisted work extraction protocol based on information gain via projective measurements [G. Francica et al., npj Quant. Inf. 3, 12 (2018)]. We prove that quantum correlations are not advantageous over classical correlations if projective measurements are considered. We go beyond the limitations of the original definition to include generalised measurements and provide an example in which this allows for a higher daemonic ergotropy. Moreover, we propose a see-saw algorithm to find a measurement that attains the maximum work extraction. Finally, we provide a multipartite generalisation of daemonic ergotropy that pinpoints the influence of multipartite quantum correlations, and study it for multipartite entangled and classical states. Full article
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Open AccessEditor’s ChoiceArticle
Non-Thermal Quantum Engine in Transmon Qubits
Entropy 2019, 21(6), 545; https://doi.org/10.3390/e21060545 - 29 May 2019
Cited by 12 | Viewed by 2146
Abstract
The design and implementation of quantum technologies necessitates the understanding of thermodynamic processes in the quantum domain. In stark contrast to macroscopic thermodynamics, at the quantum scale processes generically operate far from equilibrium and are governed by fluctuations. Thus, experimental insight and empirical [...] Read more.
The design and implementation of quantum technologies necessitates the understanding of thermodynamic processes in the quantum domain. In stark contrast to macroscopic thermodynamics, at the quantum scale processes generically operate far from equilibrium and are governed by fluctuations. Thus, experimental insight and empirical findings are indispensable in developing a comprehensive framework. To this end, we theoretically propose an experimentally realistic quantum engine that uses transmon qubits as working substance. We solve the dynamics analytically and calculate its efficiency. Full article
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Open AccessArticle
Magnetic Otto Engine for an Electron in a Quantum Dot: Classical and Quantum Approach
Entropy 2019, 21(5), 512; https://doi.org/10.3390/e21050512 - 20 May 2019
Cited by 11 | Viewed by 1674
Abstract
We studied the performance of classical and quantum magnetic Otto cycle with a working substance composed of a single quantum dot using the Fock–Darwin model with the inclusion of the Zeeman interaction. Modulating an external/perpendicular magnetic field, in the classical approach, we found [...] Read more.
We studied the performance of classical and quantum magnetic Otto cycle with a working substance composed of a single quantum dot using the Fock–Darwin model with the inclusion of the Zeeman interaction. Modulating an external/perpendicular magnetic field, in the classical approach, we found an oscillating behavior in the total work extracted that was not present in the quantum formulation.We found that, in the classical approach, the engine yielded a greater performance in terms of total work extracted and efficiency than when compared with the quantum approach. This is because, in the classical case, the working substance can be in thermal equilibrium at each point of the cycle, which maximizes the energy extracted in the adiabatic strokes. Full article
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Open AccessEditor’s ChoiceArticle
Probability Distributions with Singularities
Entropy 2019, 21(3), 312; https://doi.org/10.3390/e21030312 - 21 Mar 2019
Cited by 6 | Viewed by 1545
Abstract
In this paper we review some general properties of probability distributions which exhibit a singular behavior. After introducing the matter with several examples based on various models of statistical mechanics, we discuss, with the help of such paradigms, the underlying mathematical mechanism producing [...] Read more.
In this paper we review some general properties of probability distributions which exhibit a singular behavior. After introducing the matter with several examples based on various models of statistical mechanics, we discuss, with the help of such paradigms, the underlying mathematical mechanism producing the singularity and other topics such as the condensation of fluctuations, the relationships with ordinary phase-transitions, the giant response associated to anomalous fluctuations, and the interplay with fluctuation relations. Full article
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Open AccessArticle
Efficiency of Harmonic Quantum Otto Engines at Maximal Power
Entropy 2018, 20(11), 875; https://doi.org/10.3390/e20110875 - 15 Nov 2018
Cited by 33 | Viewed by 2002
Abstract
Recent experimental breakthroughs produced the first nano heat engines that have the potential to harness quantum resources. An instrumental question is how their performance measures up against the efficiency of classical engines. For single ion engines undergoing quantum Otto cycles it has been [...] Read more.
Recent experimental breakthroughs produced the first nano heat engines that have the potential to harness quantum resources. An instrumental question is how their performance measures up against the efficiency of classical engines. For single ion engines undergoing quantum Otto cycles it has been found that the efficiency at maximal power is given by the Curzon–Ahlborn efficiency. This is rather remarkable as the Curzon–Alhbron efficiency was originally derived for endoreversible Carnot cycles. Here, we analyze two examples of endoreversible Otto engines within the same conceptual framework as Curzon and Ahlborn’s original treatment. We find that for endoreversible Otto cycles in classical harmonic oscillators the efficiency at maximal power is, indeed, given by the Curzon–Ahlborn efficiency. However, we also find that the efficiency of Otto engines made of quantum harmonic oscillators is significantly larger. Full article
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