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1、Statisticalmechanics:AselectivereviewoftwocentralissuesJoelL.Lebowitz*DepartmentsofMathematicsandPhysics,Rutgers,TheStateUniversityofNewJersey,Piscataway,NewJersey08854-8019Igiveahighlyselectiveoverviewofthewaystatisticalmechanicsexplainsthemicroscopicoriginsofthetime-asymmetricevolution
2、ofmacroscopicsystemstowardsequilibriumandof®rst-orderphasetransitionsinequilibrium.Thesephenomenaareemergentcollectivepropertiesnotdiscernibleinthebehaviorofindividualatoms.Theyaregivenpreciseandelegantmathematicalformulationswhentheratiobetweenmacroscopicandmicroscopicscalesbecomesveryl
3、arge.[S0034-6861(99)03402-9]I.INTRODUCTIONditiveeffectsoftheactionsofindividualatoms,e.g.,thepressureexertedbyagasonthewallsofitscontainer,Naturehasahierarchicalstructure,withtime,length,whileothersareparadigmsofemergentbehavior,hav-andenergyscalesrangingfromthesubmicroscopictoingnodirec
4、tcounterpartinthepropertiesordynamicsthesupergalactic.Surprisingly,itispossible,andinofindividualatoms.Particularlyfascinatingandimpor-manycasesessential,todiscusstheselevelstantexamplesofsuchemergentphenomenaaretheir-independentlyÐquarksareirrelevantforunderstandingreversibleapproachtoe
5、quilibriumandphasetransitionsproteinfoldingandatomsareadistractionwhenstudy-inequilibrium.Bothofthesewould(orshould)beas-ingoceancurrents.Nevertheless,itisacentrallessonoftonishingiftheywerenotsofamiliar.Theirmicroscopicscience,verysuccessfulinthepastthree-hundredyears,derivationandanaly
6、sisformsthecoreofstatisticalme-thattherearenonewfundamentallaws,onlynewphe-chanics.Iwilldiscussthe®rstoftheseinSec.IIandthenomena,asonegoesupthehierarchy.ThusarrowsofsecondinSec.III.explanationsbetweendifferentlevelsalwayspointfromForamoregeneralsurveyofstatisticalmechanicsinsmallertolar
7、gerscales,althoughtheoriginofhigher-thepasthundredyears,thereaderisreferredtothelevelphenomenainthemorefundamentallower-levelotherarticlesinthissectionaswellastomyarticleinlawsisoftenveryfarfromtransparent.(Inadditionthespecialvolumecelebratingthe®rst-hundredyearsofsomeof
