耗散系统的微正则热力学与统计分裂MICROCANONICALTHERMODYNAMICSANDSTA

MICROCANONICALTHERMODYNAMICSANDSTATISTICALFRAGMENTATIONOFDISSIPATIVESYSTEMSThetopologicalstructureoftheN-bodyphasespaceD.H.E.GROSSHahn-Meitner-Institut,BereichTheorie,Glienickerstr.100,Dl4109Berlin,GermanyandFachbereichPhysikderFreienUniversitiit,Berlin,GermanyELSEVIERAMSTERDAM-LAUSANNE-NEWYORK-OXFORD-SHANNON-TOKYOPHYSICSREPORTSELSEVIERPhysicsReports279(1997)119-201Microcanonicalthermodynamicsandstatisticalfragmentationofdissipativesystems.ThetopologicalstructureoftheN-bodyphasespaceD.H.E.GrossHuhn-Meitner-Imstitut,BereichTheorie,Glienickerstr.100,014109Berlin,GermunyandFuchbereichPhysikderFreienUniversitiit,Berlin,GermanyReceivedMarch1996;editor:G.E.BrownContentsI.MICROCANONICALTHERMODYNAMICS1225.1,Nuclearfragmentations1.Introduction1225.2.Fragmentationofmultiplychargedatomic2.Basicdefinitions126clusters3.Microcanonicalthermodynamicsoffirst-orderphasetransitionsstudiedinthePottsmodel3.1.Theinterphasesurfacetension3.2.Finite-sizescaling,advantageofmicro-canonicalcomparedtocanonicalscaling3.3.Howtodistinguishphasetransitionsoffirst-orderfromcontinuousphasetransitionsinthemicrocanonicalensemble1281296.Two-dimensionalstressoflongrange:Rapidlyrotatinghotnuclei7.Conclusion131AppendixA.OnthehistoricaldevelopmentofstatisticalnuclearmultifragmentationmodelsA.1.Mathematicalpartitionvs.quantumpartition134II.STATISTICALFRAGMENTATIONUNDERFORCESOFLONGRANGE4.Introduction5.Three-dimensionalstressoflongrange:TheCoulombforce135135136AppendixB.ThemicrocanonicalensembleofNa-clustersB.I.MicrocanonicalmetropolissamplingB.2.ThebasicmicrocanonicalweightsB.3.ThemetropolispassReferences136157174178181183184187188196197AbstractThisreviewisaddressedtocolleaguesworkingindifferentfieldsofphysicswhoareinterestedintheconceptsofmicrocanonicalthermodynamics,itsrelationandcontrasttoordinary,canonicalorgrandcanonicalthermodynamics,andtogetafirsttasteofthewideareaofnewapplicationsofthermodynamicalconceptslikehotnuclei,hotatomicclustersandgravitatingsystems.0370-1573/97/$32.00Copyright01997ElsevierScienceB.V.AilrightsreservedPI1SO370-1573(96)00024-5D.H.E.Gross/PhysicsReports279(1997)119-201121MicrocanonicalthermodynamicsdescribeshowthevolumeoftheN-bodyphasespacedependsonthegloballyconservedquantitieslikeenergy,angularmomentum,mass,charge,etc.Duetotheseconstraintsthemicrocanonicalensemblecanbehavequitedifferentlyfromtheconventional,canonicalorgrandcanonicalensembleinmanyimportantphysicalsystems.Microcanonicalsystemsbecomeinhomogeneousatfirst-orderphasetransitions,orwithrisingenergy,orwithexternalorinternallong-rangeforceslikeCoulomb,centrifugalorgravitationalforces.Thus,fragmentationofthesystemintoaspatiallyinhomogeneousdistributionofvariousregionsofdifferentdensitiesand/orofdifferentphasesisagenuinecharacteristicofthemicrocanonicalensemble.Inthesecaseswhicharerealizedbythemajorityofrealisticsystemsinnature,themicrocanonicalapproachisthenaturalstatisticaldescription.Weinvestigatethismostfundamentalformofthermodynamicsinfourdifferentnontrivialphysicalcases:(I)MicrocanonicalphasetransitionsoffirstandsecondorderarestudiedwithinthePottsmodel.Thetotalenergyperparticleisanonfluctuatingorderparameterwhichcontrolsthephasewhichthesystemisin.Incontrasttothecanonicalformthemicrocanonicalensembleallowstotunethesystemcontinuouslyfromonephasetotheotherthroughtheregionofcoexistingphasesbychangingtheenergysmoothly.Theconfigurationsofcoexistingphasescarryimportantinformationsaboutthenatureofthephasetransition.Thisismoreremarkableasthecanonicalensembleisblindagainsttheseconfigurations.Itisshownthatthethreebasicquantitieswhichspecifyaphasetransitionoffirstorder-Transitiontemperature,latentheat,andinterphasesurfaceentropy-canbewelldeterminedforfinitesystemsfromthecaloricequationofstateT(E)inthecoexistenceregion.TheirvaluesarealreadyforalatticeofonlyN30*30spinsclosetotheonesofthecorrespondinginfinitesystem.ThesignificanceofthebackbendingofthecaloricequationofstateT(E)isclarified.Itisthesignalforaphasetransitionoffirstorderinafiniteisolatedsystem.(II)Fragmentationisshowntobeaspecificandgenericphasetransitionoffinitesystems.ThecaloricequationofstateT(E)forhotnucleiiscalculated.ThephasetransitiontowardsfragmentationcanunambiguouslybeidentifiedbytheanomaliesinT(E).AsmicrocanonicalthermodynamicsisafullN-bodytheoryitdeterminesallmany-bodycorrelationsaswell.Consequently,variousstatisticalmulti-fragmentcorrelationsareinvestigatedwhichgiveinsightintothedetailsoftheequilibrationmechanism.(III)Fragmentationofneutralandmultiplychargedatomicclustersisthenextexampleofarealisticapplicationofmicrocanonicalthermodynamics.Oursimulationmethod,microcanonicalMetropolisMonteCarlo,combinestheexplicitmicroscopictreatmentofthefragmentationaldegreesoffreedomwiththeimplicittreatmentoftheinternaldegreesoffreedomofthefragmentsdescribedbytheexperimentalbulkspecificheat.Thismicro-macroapproachallowsustostudythefragmentationofalsolargerfragments.Characteristicdetailsofthefissionofmultiplychargedmetalclustersfindtheirexplanationbythedifferentbulkproperties.(IV)Finally,thefragmentationofstronglyrot