Is There a Temperature?: Conceptual Challenges at High Energy, Acceleration and Complexity

325 Pages·2011·2.33 MB·English

by  Tamás Sándor Biró

Fundamental Theories of Physics
AnInternationalBookSeriesonTheFundamentalTheoriesofPhysics:
TheirClarification,DevelopmentandApplication
Volume 171
SeriesEditors
PHILIPPEBLANCHARD,Universita¨tBielefeld,Bielefeld,Germany
PAULBUSCH,UniversityofYork,Heslington,York,UnitedKingdom
BOBCOECKE,OxfordUniversityComputingLaboratory,Oxford,UnitedKingdom
DETLEFDUERR,MathematischesInstitut,Mu¨nchen,Germany
ROMAN FRIGG, London School of Economics and Political Science, London, United
Kingdom
CHRISTOPHERA.FUCHS,PerimeterInstituteforTheoreticalPhysics,Waterloo,Ontario,
Canada
GIANCARLOGHIRARDI,UniversityofTrieste,Trieste,Italy
DOMENICOGIULINI,UniversityofHannover,Hannover,Germany
GREGGJAEGER,BostonUniversityCGS,Boston,USA
CLAUSKIEFER,UniversityofCologne,Cologne,Germany
KLAASLANDSMAN,RadboudUniversiteitNijmegen,Nijmegen,TheNetherlands
CHRISTIANMAES,K.U.Leuven,Leuven,Belgium
HERMANNNICOLAI,Max-Planck-Institutfu¨rGravitationsphysik,Golm,Germany
VESSELINPETKOV,ConcordiaUniversity,Montreal,Canada
ALWYNVANDERMERWE,UniversityofDenver,Denver,USA
RAINERVERCH,Universita¨tLeipzig,Leipzig,Germany
REINHARDWERNER,LeibnizUniversity,Hannover,Germany
CHRISTIANWU¨THRICH,UniversityofCalifornia,SanDiego,LaJolla,USA
Forfurthervolumes:
http://www.springer.com/series/6001

Tama´s Sa´ndor Biro´
Is There a Temperature?
Conceptual Challenges at High Energy,
Acceleration and Complexity
123
Tama´sSa´ndorBiro´
MTAKFKIRMKI
HungarianAcademyofSciences
Budapest,Hungary
[email protected]
ISBN978-1-4419-8040-3 e-ISBN978-1-4419-8041-0
DOI10.1007/978-1-4419-8041-0
SpringerNewYorkDordrechtHeidelbergLondon
LibraryofCongressControlNumber:2011921336
(cid:2)c SpringerScience+BusinessMedia,LLC2011
Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten
permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York,
NY10013, USA),except forbrief excerpts inconnection with reviews orscholarly analysis. Usein
connectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,
orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.
Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyare
notidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubject
toproprietaryrights.
Coverdesign:eStudioCalamarS.L.
Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
To Tu¨nde, Szilvia,Re´ka, Ga´borandKati.

Preface
Yet another book about thermodynamics? Wherefore? This almost 200-year-old
physicssubjectisbeingdiscussedindepthandpresentedinaplethoraoftextbooks
extensively. It is not my intention to add one to this number. It is the experience
in modernresearchproblemsdealingwith matterunderextremeconditionswhich
challengesmetowriteabookaboutthistopic.Physicalmatterathighenergy,veloc-
ityandmomenta,underextremeaccelerationordeceleration,orbyanotherparticu-
larcircumstance,suchasunusualcomplexity,doesbehavestrangely.Talkingabout
extremely high or low, by the familiar thermometernot measurable temperatures,
leads us notonly to the question,what is the temperatureof such matter, but also
to thequestion,whethertheveryconceptofabsolutetemperatureisapplicable:Is
thereatemperatureatall?
The more important this question becomes since the “social” disciplines of
physics,likebiologicalphysics,econophysics,sociologicalmodelsstartedtoapply
mathematical models and concepts originally devised for the study of “ordinary,”
i.e.atomicmatter.Thesegeneralizedstatisticalandstochasticmodelsapplyquanti-
tiesanalogoustothephysicalenergy,totheentropicmeasureoforderanddisorder,
and to the associated concept of absolute temperature. By such applications of
physics, however, the exception seems to be the rule: most studied distribution
propertiesarepeculiarfromtheclassicalthermodynamicsviewpoint.Togiveanex-
ample,theBlack–Sholesmodel,describingpricingstrategiesforderivativefinancial
transactions,1ismathematicallyaclassicaldiffusionmodel,liketheFokker–Planck
equation.Meanwhile,it turned outthat morerealistic modelsdescribingthe price
fluctuations do show a fat tail, namely a non-Gaussian distribution. Such tails,
frequentlyoccurringaspower-lawtails, canbedescribedasaresultofanomalous
diffusion.The generaltheory dealing with such distributions, as classical thermo-
dynamicsdoeswiththecanonicalexponentialenergydistribution,isinitsmaking
currently.Oneofhertentativenamesisnon-extensivethermodynamics.
1 TheBankofSwedenPrizeinEconomicSciencesinMemoryofAlfredNobelwasawardedto
RobertC.MertonandMyronS.Sholesin1997,whoworkedoutthismodelinclosecollaboration
withFisherBlack.
vii
viii Preface
However,thisbookisnotanotherintroductionintonon-extensivethermodynam-
icseither.Therearegoodbooksdevotedtothistask.Theintentionhereistopresent
basicconceptsattheveryheartofstatisticalphysicsastheyarechallengedinhigh
energynuclearandparticle physicsby phenomenalike energydistributionof par-
ticlesirradiatedfromafireballmimickingtheBigBanginlittle,likeaquiteformal
use of absolute temperature as a parameter of higher than four-dimensional ob-
jectsorliketheparticularbehaviorofcolorednoiseinthedynamicsofelementary
fields. By doing so we particularly concentrate to the recurring question whether
allthe“anomalous”thermodynamicsbehaviorisjustafinite-sizefinite-timeeffect,
or it survives the (in several cases only theoretical) limit of a large number of
degree of freedom, commonly called the “thermodynamical limit.” This question
canpresentlybeansweredinthemathematicalframework;theanswersinphysical
experimentsseemtobedelegatedtothefuture.Notably,alsothequestion:Isthere
atemperature?intheseexotic,highlyenergeticphysicalphenomena.
BudapestandPiliscsaba Tama´sSa´ndorB´ıro´
August2009–September2010
Acknowledgments
There are due acknowledgments for a number of persons. The most important
catalyzing event to start writing this book was a general question on the ΣΦ
(Statisticsin Physics)Conference,inKolymbari,Crete, in2008fromanEditorof
SpringerVerlagtotheparticipants:whetheranyonehadanideatowriteagood,in-
terestingphysicsbook.Iattendedthatconferenceandsubconsciouslybeganthink-
ing abouthow to confrontsome unclearedusage of statistical physics methodsin
theareaofhigh-energyphysics,morecloselyheavy-ioncollisions,withchallenging
questionsofcontemporarystatisticalphysics–whichtheconferencewaspartially
organizedabout.IrespondedtotheinquirythatIpossiblywouldhaveanidea.
One year later there came an e-mail from Jeanine Burke, of Springer Verlag,
enquiring if I still had the idea to write a book about challenges at the merge of
high-energyandstatisticalphysics.Infact,Iwasalreadyoccupiedwiththewriting
of another book, about variational principles in the basic laws of physics, at that
time. Nevertheless, I responded positively and sent an outline of the contents, a
quicklywritten introduction,andfilled outa detailed questionnaireto the Editors.
They then selected this idea to be a project, we signed a contract, and so I began
workonit.IhavetothanktheSpringerVerlagformotivatingmetoreallyworkon
thisproject,andtoRebeccaNisonforescortingmyauthorship.
FrommycolleaguesinPhysicsIthankfirstofallProf.ConstantinoTsallis,who–
besidesbeingawell-knownpromoterofthenewviewonthepossibleextensionof
thermodynamicsandstatisticalphysicsbeyondtheclassicalgrounds–alsoperson-
allysupportedmyeffortstounderstandandgeneralizetheclassicalconceptsinmy
ownwayandtopresentpartoftheproblemsfrommyparticularcornerofviewin
severaldiscussions.Dr.GiorgioTorrierifromtheFrankfurtUniversityhelpedmea
lotongettingintocontactwithworksonclassicalandstring-theoryinducedhigher-
dimensionalgravityandthiswaytoputtheperspectiveonreallyfar-stretchedtheo-
reticalchallengesontheconceptsoftemperatureandentropy.Furthermore,Ithank
Prof.Miklo´sGyulassyfromColumbiaUniversityforhispatientconversationswith
me and for his critical remarks about this topic. I have learned a lot about which
questionswouldbeimportanttoanswer.
ix