Table Of ContentQuantum Thermodynamics
An introduction to the thermodynamics of quantum information
Quantum Thermodynamics
An introduction to the thermodynamics of quantum information
Sebastian Deffner
University of Maryland, Baltimore County (UMBC), Baltimore, Maryland, USA
Steve Campbell
Trinity College, Dublin, Ireland
Morgan & Claypool Publishers
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ISBN 978-1-64327-658-8(ebook)
ISBN 978-1-64327-655-7(print)
ISBN 978-1-64327-656-4(mobi)
DOI 10.1088/2053-2571/ab21c6
Version:20190701
IOPConcisePhysics
ISSN2053-2571(online)
ISSN2054-7307(print)
AMorgan&ClaypoolpublicationaspartofIOPConcisePhysics
PublishedbyMorgan&ClaypoolPublishers,1210FifthAvenue,Suite250,SanRafael,CA,
94901,USA
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Quidquid praecipies, esto brevis.
(Horaz, Ars poetica 335)
Contents
Preface ix
Acknowledgments xiii
Author biographies xv
1 The principles of modern thermodynamics 1-1
1.1 A phenomenological theory of heat and work 1-1
1.1.1 The five laws of thermodynamics 1-2
1.1.2 Finite-time thermodynamics and endoreversibility 1-8
1.2 The advent of Stochastic Thermodynamics 1-10
1.2.1 Microscopic dynamics 1-11
1.2.2 Stochastic energetics 1-13
1.2.3 Jarzynski equality and Crooks theorem 1-14
1.3 Foundations of statistical physics from quantum entanglement 1-18
1.3.1 Entanglement assisted invariance 1-19
1.3.2 Microcanonical state from envariance 1-19
1.3.3 Canonical state from quantum envariance 1-21
1.4 Work, heat, and entropy production 1-24
1.4.1 Quantum work and quantum heat 1-24
1.4.2 Quantum entropy production 1-27
1.4.3 Two-time energy measurement approach 1-28
1.4.4 Quantum fluctuation theorem for arbitrary observables 1-33
1.4.5 Quantum entropy production in phase space 1-35
1.5 Checklist for ‘The principles of modern thermodynamics’ 1-37
1.6 Problems 1-37
References 1-38
2 Thermodynamics of quantum systems 2-1
2.1 Quantum thermometry 2-1
2.1.1 Thermometry for harmonic spectra 2-3
2.1.2 Optimal thermometers 2-5
2.2 Quantum heat engines—engines with atomic working fluids 2-6
2.2.1 The Otto cycle: classical to quantum formulation 2-6
2.2.2 A two-level Otto cycle 2-8
2.2.3 Endoreversible Otto cycle 2-12
vii
QuantumThermodynamics
2.3 Work extraction from quantum systems 2-18
2.3.1 Work extraction from arrays of quantum batteries 2-19
2.3.2 Powerful charging of quantum batteries 2-23
2.4 Quantum decoherence and the tale of quantum Darwinism 2-24
2.4.1 Work, heat, and entropy production for dynamical semigroups 2-24
2.4.2 Entropy production as correlation 2-27
2.4.3 Quantum Darwinism: emergence of classical objectivity 2-29
2.5 Checklist for ‘Thermodynamics of quantum systems’ 2-33
2.6 Problems 2-33
References 2-35
3 Thermodynamics of quantum information 3-1
3.1 Quantum thermodynamics of information 3-2
3.1.1 Thermodynamics of classical information processing 3-2
3.1.2 A quantum sharpening of Landauer’s bound 3-6
3.1.3 New Landauer bounds for nonequilibrium quantum systems 3-8
3.2 Performance diagnostics of quantum annealers 3-10
3.2.1 Fluctuation theorem for quantum annealers 3-11
3.2.2 Experimental test on the D-Wave machine 3-13
3.3 Kibble–Zurek scaling of irreversible entropy 3-14
3.3.1 Fundamentals of the Kibble–Zurek mechanism 3-16
3.3.2 Example: the Landau–Zener model 3-17
3.3.3 Kibble–Zurek mechanism and entropy production 3-18
3.4 Error correction in adiabatic quantum computers 3-21
3.4.1 Quantum error correction in quantum annealers 3-22
3.4.2 Adiabatic quantum computing—a case for shortcuts 3-23
to adiabaticity
3.4.3 Counterdiabatic Hamiltonian for scale-invariant driving 3-25
3.5 Checklist for ‘Thermodynamics of quantum information’ 3-31
3.6 Problems 3-31
References 3-33
Epilogue 4-1
viii
Preface
What is physics? According to standard definitions in encyclopedias physics is a
science that deals with matter and energy and their interactions1. However, as
physicists what is it that we actually do? At the most basic level, we formulate
predictions for how inanimate objects behave in their natural surroundings. These
predictions are based on our expectation that we extrapolate from observations of
the typical behavior. If typical behavior is universally exhibited by many systems of
the same ‘family’, then this typical behavior is phrased as a law.
Take for instance the infamous example of an apple falling from a tree. The same
behaviorisobservedforanykindoffruitandanykindoftree—thefruit‘always’falls
fromthetreetotheground.Well,actuallythesamebehaviorisobservedforanyobject
that is let loose above the ground, namely everything will eventually fall towards the
ground. It is this observation of universal falling that is encoded in the law of gravity.
Mosttheoriesinphysicsthenseektounderstandthenitty-grittydetails,forwhich
finerandmoreaccurateobservationsareessential.Generally,weendupwithmore
and more fine-grained descriptions of nature that are packed into more and more
sophisticatedlaws.Forinstance,fromclassicalmechanicsoverquantummechanics
toquantumfieldtheoryweobtainanevermoredetailedpredictionforhowsmaller
and smaller systems behave.
Realizing this typical mindset of physical theories, it does not come as a big
surprise that many students have such a hard time wrapping their minds around
thermodynamics:
Thermodynamicsis aphenomenologicaltheory todescribetheaveragebehavior
of heat and work.
Asaphenomenologicaltheory,thermodynamicsdoesnotseektoformulatedetailed
predictionsforthemicroscopicbehaviorofsomephysicalsystems,butratheritaims
to provide the most universal framework to describe the typical behavior of all
physical systems.
‘Reflections on the motive power of fire’. The origins of thermodynamics trace
back to the beginnings of the industrial revolution [6]. For the first time, mankind
started developing artificial devices that contained so many moving parts that it
becamepracticallyimpossibletodescribetheir behaviorinfull detail.Nevertheless,
the first devices, steam engines, already proved to be remarkably useful and
dramatically increased the effectiveness of productive efforts.
The founding father of thermodynamics is undoubtedly Sadi Carnot. After
Napoleon had been exiled, France started importing advanced steam engines from
Britain, which made Carnot realize how far France had fallen behind its adversary
fromacrossthechannel.Quiteremarkably,asmallnumberofBritishengineers,who
totallylackedanyformalscientificeducation,hadstartedtocollectreliabledataabout
theefficiencyofmanytypesofsteamengines.However,itwasnotatallclearwhether
there was an optimal design and what the highest efficiency would be.
1Thisandsimilardefinitionscanbefound,forinstance,inMerriam-Webster.
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