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1、Physics127a:ClassNotesLecture1:TheFundamentalPostulateAfterageneraldiscussionofthescopeofStatisticalMechanicsIintroducedtheFundamentalPostulateofequalaprioriprobabilities:Anisolatedsysteminequilibriumisequallylikelytobefoundinanyofthemicrostatesaccessibletoit.Thisp
2、hraseintroducesanumberofideasthatwillbedevelopedfurtherinfuturelectures:System:partoftheuniverseweareinterestedin,onlyweaklycoupledtotherestoftheuniversesothatthedynamicsisdominatedbytheinternalinteractions.Isolated:idealization—eliminateallexternalinfluences,inpart
3、icularnoforces,energyflux,particlefluxetc.sothatquantitiesconservedbytheinternaldynamicsarestrictlyconstantfortheisolatedsystem.Equilibrium:waitlongenoughsothatalltransientbehaviordiesout,andmeasurementsofmacroscopicquantitiesbecometimeindependent.Microstate:acomplet
4、emicroscopicspecificationoftheparticlessothatthedynamicsofthewholesystemcouldbefollowedinprinciple.Basicallywhereparticlesare,andtheirvelocities,foraclassicalsystem,andthequantumstate(wavefunction)foraquantumsystem.Likely:wearedealingwithprobabilities!Tomakethisidea
5、preciseforasinglesystem,weintroducethenotionofanensemble—ahugenumberofessentialrepetitionsofthesystem(i.e.macroscopicallythesame,butmaybedifferinginmicroscopicpropertiessuchasinitialconditionsoftheparticles).Theprobabilityofamicrostateisthenthefractionofthememberso
6、ftheensembleinwhichthemicrostateisrepresented.Weusuallyassumethattheaveragedoneinatypicalexperiment,whichisusuallyatimeaverageonasinglesystem,arewellpredictedbyensembleaverages.Thisreliesonanideaknownasergodicity.Accessible:consistentwiththemacroscopicconstraints,u
7、suallythevaluesoftheconservedquantitiese.g.fixedenergy,numberofparticlesetc.,butmayalsoincludeothers,e.g.an“orderparameter”definingthestatebelowaphasetransition,ortheseparationoftheendsofalongpolymer.Thefundamentalassumptionreducestheprobabilityoffindingamacroscopicco
8、nfigurationinanisolatedsystemtocountingthenumberofmicrostatesconsistentwiththemacroscopicconfiguration.1Physics127a:ClassNotesLecture2:ASimpleProba
