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1、ThispageintentionallyleftblankCHAOSANDCOARSEGRAININGINSTATISTICALMECHANICSWhilestatisticalmechanicscandescribetheequilibriumstateofsystemswithmanydegreesoffreedom,anddynamicalsystemscanexplaintheirregularevolutionofsystemswithfewdegreesoffreedom,newtoolsareneededtostudytheevolutionofsystemswithman
2、ydegreesoffreedom.Thisbookpresentsthebasicaspectsofchaoticsystems,withemphasisonsystemscomposedofahugenumberofparticles.Thefirstpartofthebookintroducesthebasicconceptsofchaoticdynamics.Thebookthenmovesontoexploretheroleofergodicityandchaosforthevalidityofstatisticallaws.Thelastpartofthebookisdevote
3、dtothetreatmentofproblemscharacterizedbythepresenceofmorethanonesignificantscale.Inaddition,theauthorsalsodiscusstherelevancethatmanydegreesoffreedom,coarse-grainingprocedure,andinstabilitymechanisms,haveinjustifyingastatisticaldescriptionofmacroscopicbodies.Thebookintroducesthetoolstocharacterizet
4、henon-asymptoticbehaviorsofchaoticsystems.Thistextwillbeofinteresttoresearchersandgraduatestudentsinstatisticalmechanicsandchaos.PatriziaCastiglioneisaResearcherattheInstitutdesNanosciencesdeParis.Hermainresearchtopicsaredynamicalsystemstheory,quantumandclassicchaos,turbulence,andthephysicsofcolor
5、sappliedtothestudyofartwork.MassimoFalcioniisaResearcherattheUniversityofRome“LaSapienza.”Hisresearchfocusesonelementaryparticlephysics,dynamicalsystems,andstatisticalmechanics.AnnickLesneisaCNRSResearcherattheLaboratoiredePhysiqueTh´eoriquedelaMati`ereCondens´ee(CNRS-Paris6)andtemporarilyattheIns
6、titutdesHautesEtudesScientifiques.Herresearchliesinrenormalizationmethodsfordynamical´systems,non-equilibriumstatisticalphysics,andapplicationsofdynamicalsystemstheoryandstatisticalmechanicstobiologicalsystems.AngeloVulpianiisaProfessorofTheoreticalPhysicsattheUniversityofRome“LaSapienza,”andisaFel
7、lowoftheInstituteofPhysics.Hisresearchinterestsarestatisticalmechanics,dynamicalsystems,turbulence,transport,andreaction-diffusioninfluids.CHAOSANDCOARSEGRAININGINSTATISTICALMECHANICSPATRIZIACASTIGLIONEInstitutdes