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