The Physics of Computing

142 Pages·2021·3.048 MB·English

by  Luca Gammaitoni

Luca Gammaitoni
The Physics
of Computing
The Physics of Computing
Luca Gammaitoni
The Physics of Computing
LucaGammaitoni
NiPSLaboratory
UniversitàdiPerugia
Perugia,Italy
ISBN978-3-030-87107-9 ISBN978-3-030-87108-6 (eBook)
https://doi.org/10.1007/978-3-030-87108-6
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Preface
Thisbookisaboutthephysicsofcomputingthatisnotthesameasthephysicsof
computers.
Indeed,therearemanygoodbooksthatdiscussindetailthefunctioningofmodern
computers,withspecificreferencetothephysicalprinciplesthatruletheiroperations
andthisbookisnotoneofthem.Here,wearenotgoingtogothroughanydescription
ofsemiconductormaterialsorleakagecurrentsinthelastgenerationoffield-effect
transistors. You will not be bored with the description of the MOS capacitor or
withthelithographictechniquerequiredtosqueezemoretransistorsinsidethesame
microprocessor.Ifyouareinterestedinthesearguments,pleasedonotreadthisbook.
Howisthephysicsof computingdifferentfromthephysicsofcomputers?Well,
itisliketosaythatwearegoingtotalkaboutthephysicsofplanetarymotion;i.e.
wearenotinterestedinthedynamicsofJupiterorMars,butwewanttofocusour
attentiontothoseprinciplesthatgovernthemotionofanyoftheplanets,ignoring
the differences among them. In this sense, we are interested in dealing with the
fundamentalunderlyingprinciples(ifany)thatcharacterizethecomputingmachines
existed,existingand,bydefinitionof“fundamentalunderlyingprinciples”,thatwill
everexistinfuture.
Suchanexaggeratedambitionwouldrequireaclearandstrongdefinitionofwhat
wemeanwiththewords“computing”and“computer”.Well,wewilltrytogetaway
withthefollowingdefinitions:“computingiswhatacomputerdoes”and“computer
is a device that can be instructed to carry out sequences of arithmetic or logical
operationsautomatically”(source:Wikipedia).Andwewillgiveforgrantedthatthe
readerknowswhatanarithmeticorlogicaloperationis,althoughwewillcomeback
tothispointlaterinthebook.Basedonthesedefinitions,wecansaythatcomputing
ismerelycarryingonasequenceofarithmeticand/orlogicoperations.
Thus,inthisbook,wewilldiscussthefundamentalphysicsprinciplesthatrule
ANYphysicaldevicebuilttocarryonarithmeticand/orlogicoperations.
Perugia,Italy LucaGammaitoni
v
Acknowledgements
The author owes a debt of gratitude to all friends, colleagues, collaborators and
studentsofNoiseinPhysicalSystems(NiPS)LaboratoryattheUniversityofPerugia,
for developing the vision which underlies the writing of this book. In particular,
hewishestothankMarkusButtiker,GiovanniCarlotti,FrancescoCottone,Davide
Chiuchiù,AlessandroDiMichele,CristinaDiamantini,MiquelLopez-Suarez,Igor
Neri,MarcoMadami,FabioMarchesoni,MaurizioMattarelli,CarloPresilla,Carlo
Trugenberger,HeliosVoccaandAngeloVulpiani.SpecialthankstoIgorNerifora
carefulreadingofthems.
vii
Contents
1 ComputingwithDevices ....................................... 1
1.1 WhatDoWeMeanwithComputing? ....................... 1
1.2 CalculusMeansStone .................................... 4
1.3 OnComputingDevices ................................... 6
1.4 UniversalMachines ....................................... 8
1.5 InterestingQuestions ..................................... 9
References .................................................... 10
2 ThePhysicsofDigitalComputing ............................... 11
2.1 Digits ................................................... 11
2.2 BinaryDigits ............................................ 13
2.3 BinarySwitches .......................................... 14
2.4 LogicSwitches .......................................... 17
2.5 LogicGates ............................................. 20
2.6 LogicGatesMadebyLogicSwitches ....................... 25
2.7 ADynamicalModel ...................................... 28
2.8 TheSwitch .............................................. 30
References .................................................... 35
3 WhatisFriction ............................................... 37
3.1 EnergyConservation ...................................... 37
3.2 BrownianMotion ........................................ 39
3.3 Langevin’sApproach ..................................... 40
3.4 FluctuatingCantilever .................................... 44
3.5 FluctuationandDissipationComeTogether .................. 46
3.6 ThermodynamicsforEverybody ............................ 49
3.7 EnergyandEntropyatSmallScales ......................... 53
3.8 FrictionatSmallScales ................................... 57
References .................................................... 58
ix
x Contents
4 ThePhysicsofSmall-ScaleSwitches ............................ 59
4.1 LogicSwitchesasThermodynamicSystems ................. 59
4.2 ADigression:EnergyDissipationisanIllusion? .............. 60
4.3 TheSwitchDynamicsinthePresenceofFluctuations ......... 62
4.4 Combinational Switches: The Switch in the Presence
ofFluctuations ........................................... 65
4.5 Sequential Switches: The Switch in the Presence
ofFluctuations ........................................... 66
References .................................................... 68
5 FundamentalEnergyLimitsinComputation .................... 69
5.1 HowMuchEnergyDoesItTaketoSwitchandWhyThis
isImportant? ............................................ 69
5.2 CombinationalSwitches:MinimumDissipatedEnergy ........ 70
5.3 SequentialSwitches:MinimumDissipatedEnergy ............ 73
5.4 BitReset:MinimumDissipatedEnergy ...................... 75
5.5 MinimumDissipatedEnergy:HowFarAreWe? .............. 78
References .................................................... 80
6 StoringData .................................................. 83
6.1 Memories:HowDoTheyWork? ........................... 83
6.2 MemoryDynamics ....................................... 85
6.3 FundamentalEnergyLimitsforMemoryStorage ............. 86
6.4 FundamentalLimitsforMemoryPreservation ................ 90
6.5 BeyondDigitalMemories ................................. 91
References .................................................... 92
7 WhatAboutInformation? ..................................... 93
7.1 TheBigPicture .......................................... 93
7.2 Information:WhatisIt? ................................... 94
7.3 Landauer’sPrinciple:LongStoryShort ...................... 95
7.4 Sub-k TMicroelectromechanicalIrreversibleORLogic
B
Gate .................................................... 97
References .................................................... 101
8 CloudComputingandDataTransmission ....................... 103
8.1 ANewNameforanOldSituation .......................... 103
8.2 SignalTransmission ...................................... 104
8.3 MinimumEnergyforTransmittingOneBit .................. 106
Reference ..................................................... 108
9 AnalogComputing ............................................ 109
9.1 WhatisAnalogComputing? ............................... 109
9.2 AnalogComputersCameFirst ............................. 111
9.3 ElectronicAnalogComputers .............................. 113
Contents xi
9.4 Energy DissipationandEntropy Reduction inAnalog
Computing .............................................. 116
References .................................................... 117
10 ComputingintheQuantumRegime ............................. 119
10.1 HowisQuantumComputingDifferentfromClassical
Computing .............................................. 119
10.2 QuantumComputationandEnergyDissipation ............... 121
10.3 QuantumBinarySwitches ................................. 123
10.4 QuantumLimitinComputingSpeed ........................ 124
10.5 Quantum Limit to Entropy Reduction in Analog
ComputingSystems ...................................... 125
References .................................................... 127
11 TheFutureofComputingandSociety ........................... 129
11.1 ReflectionsontheComputingEra .......................... 129
11.2 FromtheIntroductionofDigitalTechnologytoBigData ....... 130
11.3 BigDataandAIfortheCreationofNewKnowledge .......... 132
11.4 TheSurveillanceSocietyNightmare ........................ 134
11.5 AreDigitalDataInevitable? ............................... 135
11.6 ComputersoftheFuture:TheAtomsStrikeBack ............. 136
References .................................................... 138
Chapter 1
Computing with Devices
Itisunworthyofexcellentmentolosehourslikeslavesinthe
laborofcalculationwhichcouldsafelyberelegatedtoanyone
elseifmachineswereused.
GottfriedWilhelmLeibnitz(1646–1716)
Abstract Computingisanaturalactformostofus,nowadays.However,ithasnot
been so for many years, for many people, along the history of humankind. In this
chapter,wediscusswhatdowemeanwithcomputingandhowthisactivitycanbe
donewiththehelpofdevices.Theroleofthischapteristolaythefoundationsforthe
developmentofatreatmentofcomputationalprocessesintermsofthefunctioning
ofthephysicalsystemsthattheseprocessesarecalledupontocarryout.
1.1 WhatDoWeMeanwith Computing?
The term computing comes from the Latin computare, a word composed by the
union of cum (with) and putare (to evaluate in quantitative sense). Together they
meanto“evaluatequantitativelythings”,strictsynonymousofcalculating,another
Latinoriginatedwordthatwewillconsiderlateron.So,basedonthisunderstanding,
wecouldsaythatcomputingsomethinghastodowithdealingwiththequantitative
aspectsofthings.
How do we do that? Since when we were kids, we had to deal with numbers.
A number represents a feature of specific properties of ensembles of things. For
example: a bunch of cookies in a basket comes with some properties. They are
sweet,theymaybewarmorcold,theymaybelightorheavyandtheymayfewor
many.Thesepropertiesareevaluatedherequalitativelybut,ifwewanttobemore
precise,wecouldspecifyhowmuchthesepropertiesareinplace.Givenourbasketof
cookies,wecansaythattheyarewarmatthetouch(morepreciselytheirtemperature
is42°C),lightifweraisethem(morepreciselytheirweightis320g),theyaremany
(morepreciselytheyareten).Howdoweestablishthesequantities?
This can be done once we set a unit of measure and a method to compare the
same property in different baskets. Comparing is clearly the first attempt to deal
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L.Gammaitoni,ThePhysicsofComputing,
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