统计动力学

1Introduction
1.1BibliographicalNotesBN1
2States,DynamicalFunctions,Evolution
2.1GeneralConsiderations
2.2MacroscopicDynamicalSystems
2.3MicroscopicDynamicalSystems
2.4SystemsofInteractingParticles
2.5BibliographicalNotesBN2
3GeneralFormalismofStatisticalMechanics
3.1MacroscopicPhysicsandMicroscopicPhysics
3.2ThePhaseSpaceDistributionFunction
3.3EquilibriumStates
3.4BibliographicalNotesBN3
4ReducedDistributionFunctionsandCorrelationFunctions
4.1ClassificationofDynamicalFunctions
4.2ReducedDistributionFunctions
4.3EvohitionoftheReducedDistributionFunctions.
4.4CorrelationFunctions
4.5EvolutionoftheCorrelationFunctions
4.6BibliographicalNotesBN4
5TheMeanFieldApproximation
5.1WeaklyCoupledSystems
5.2FreeParticleDynamics.
5.3TheVlasovEquation
5.4TheLinearizedVlasovEquation
5.5Conclusions.
5.6BibliographicalNotesBN5
6TheWeakCouplingKineticEquation
6.1TheMasterEquation
6.2TheLandauEquation
6.3ExplicitformoftheLandaucollisionterm
6.4Conclusion
6.5Appendix.TheCauchyIntegral
6.6BibliographicalNotesBN6
7KineticEquationforDiluteGases
7.1TheDiluteGasOrdering.
7.2TheBoltzmannEquation
7.3ImplementationoftheBoltzmannEquation
7.4BibliographicalNotesBN7
8KineticEquationforPlasmas
8.1ThePlasmaOrdering
8.2TheIntegralEquationfortheCorrelation
8.3ThePlasmaKineticEquation
8.4PropertiesoftheBalescu-LenardEquation
8.5BibliographicalNotesBN8
9PropertiesofKineticEquations
9.1TheConceptofaKineticEquation
9.2StochasticEquationsofEvolution
9.3NatureoftheCollisionProcess
9.4IrreversibilityandEntropy
9.5SpatiallyInhomogeneousSystems
9.6TheCollisionalInvariants
9.7BibliographicalNotesBN9
10HydrodynamicsandTransport
10.1TheHydrodynamicQuantities
10.2TheHydrodynamicalBalanceEquations
10.3DiffusionandHeatConduction
10.4TheHermitianMomentExpansion
10.5DerivationoftheTransportEquations
10.6PropertiesoftheTransportCoefficients
10.7EntropyandTransport
10.8Conclusions
10.9BibliographicalNotesBN10
11TransportandAutocorrelationFunctions
11.1Introduction
11.2MeanSquareDisplacementandDiffusion
11.3TheLangevinEquations
11.4TheHybridKineticEquation
11.5TheGreen-KuboFormulae
11.6BibliographicalNotesBN11
12RandomWalksandTransport
12.1ClassicalRandomWalks
12.2ContinuonsTimeRandomWalks(CTRW)
12.3TheStandardLong-TailCTRW(SLT-CTRW)
12.4SLT-CTRW:TheDensityProfile
12.5SLT-CTRW:TheNon-MarkovianDiffusionEquation
12.6Markovianvs.Non-MarkovianEvolution
12.7Appendix.StableProbabilityDistributionFunctions
12.8BibliographicalNotesBN12
13CriticalPhenomena
13.1OverviewoftheEquilibriumCriticalPhenomena
13.2Percolation
13.3One-dimensionalSystems
13.4ScalingTheoryofPercolation
13.5PercolationClustersandFractals
13.6BibliographicalNotesBN13
14TransportonPercolationStructures
14.1ElectricalConductivityandPercolation
14.2DiffusionandPercolation
14.3StrangeDiffusionontheInfiniteCluster
14.4Conclusions
14.5BibliographicalNotesBN14
15ChaosandTransport
15.1TheStandardMap
15.2ThePerron-FrobeninsOperator
15.3TheDiffusiveRegime
15.4TheSubdiffusiveRegime
15.5Appendix.TransformationoftheResolvent
15.6BibliographicalNotesBN15
16Conclusions
16.1TheStatusofStatisticalDynamics
16.2TowardaGrandTheoryofIrreversibility?
16.3"StochasticStatistical"Dynamics
16.4BibliographicalNotesBN16
Index