Stochastic Processes and Brownian随机过程与Brownian 运动

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1、Chapter1StochasticProcessesandBrownianMotionEquilibriumthermodynamicsandstatisticalmechanicsarewidelyconsideredtobecoresubjectmatterforanypracticingchemist[1].Thereareplentyofreasonsforthis:•Agreatmanychemicalphenomenaencounteredinthelaboratoryarewelldescribedbyequilibrium

2、thermodynamics.•Thephysicsofchemicalsystemsatequilibriumisgenerallywellunderstoodandmathematicallytractable.•Equilibriumthermodynamicsmotivatesourthinkingandunderstandingaboutchemistryawayfromequilibrium.Thislastpoint,however,raisesaseriousquestion:howwelldoesequilibriumth

3、ermodynamicsreallymotivateourunderstandingofnonequilibriumphenomena?Isitreasonableforanorganometallicchemisttoanalyzeacatalyticcycleintermsofrate-lawkinetics,orforabiochemisttotreattheconcentrationofasoluteinanorganelleasabulkmixtureofcompounds?Undermanycircumstances,equil

4、ibriumthermodynamicssuffices,butagrowingnumberofoutstandingproblemsinchemistry–fromelectrontransferinlight-harvestingcomplexestothechemicalmechanismsbehindimmunesystemresponse–concernprocessesthatarefundamentallyoutofequilibrium.Thiscourseendeavorstointroducethekeyideasthath

5、avebeendevelopedoverthelastcenturytodescribenonequilibriumphenomena.Theseideasarealmostinvariablyfoundeduponastatisticaldescriptionofmatter,asintheequilibriumcase.However,sincenonequilibriumphenomenacontainamoreexplicittime-dependencethantheirequilibriumcounterparts(consid

6、er,forexample,thedecayofanNMRsignalortheprogressofareaction),theprobabilistictoolswedevelopwillrequiresometime-dependenceaswell.Inthischapter,weconsidersystemswhosebehaviorisinherentlynondeterministic,orstochastic,andweestablishmethodsfordescribingtheprobabilityoffindingthe

7、systeminaparticularstateataspecifiedtime.1Chapter1.StochasticProcessesandBrownianMotion21.1MarkovProcesses1.1.1ProbabilityDistributionsandTransitionsSupposethatanarbitrarysystemofinterestcanbeinanyoneofNdistinctstates.Thesystemcouldbeaproteinexploringdifferentconformationals

8、tates;orapairofmoleculesoscillatingbetweena“reactants”stateanda“products”state;oranysyste