统计力学

1.BasicPrinciples

1.1Introduction

1.2ABriefExcursionintoProbabilityTheory

1.2.1ProbabilityDensityandCharacteristic.Functions

1.2.2TheCentralLimitTheorem.

1.3EnsemblesinClassicalStatistics.

1.3.1PhaseSpaceandDistributionFunctions

1.3.2TheLiouvilleEquation

1.4QuantumStatistics

1.4.1TheDensityMatrixforPureandMixedEnsembles

1.4.2TheVonNeumannEquation.

*1.5AdditionalRemarks

*1.5.1TheBinomialandthePoissonDistributions

*1.5.2MixedEnsemblesandtheDensityMatrixofSubsystems

Problems

2.EquilibriumEnsembles

2.1IntroductoryRemarks

2.2MicrocanonicalEnsembles

2.2.1MicrocanonicalDistributionFunctionsandDensityMatrices

2.2.2TheClassicalIdealGas

*2.2.3Quantum.mechanicalHarmonicOscillatorsandSpinSystems

2.3Entropy

2.3.1GeneralDefinition

2.3.2AnExtremalPropertyoftheEntropy

2.3.3EntropyoftheMicrocanonicalEnsemble

2.4TemperatureandPressure

2.4.1SystemsinContact：theEnergyDistributionFunctionDefinitionoftheTemperature

2.4.20ntheWidthsoftheDistributionFunctionsofMacroscopicQuantities

2.4.3ExternalParameters：Pressure

2.5PropertiesofSomeNon-interactingSystems

2.5.1TheIdealGas

*2.5.2Non-interactingQuantumMechanicalHarmonicOscillatorsandSpins

2.6TheCanonicalEnsemble

2.6.1TheDensityMatrix

2.6.2Examples：theMaxwellDistributionandtheBarometricPressureFormula

2.6.3TheEntropyoftheCanonicalEnsembleandItsExtremalValues

2.6.4TheVirialTheoremandtheEquipartitionTheorem

2.6.5ThermodynamicQuantitiesintheCanonicalEnsemble

2.6.6AdditionalPropertiesoftheEntropy

2.7TheGrandCanonicalEnsemble

2.7.1SystemswithParticleExchange

2.7.2TheGrandCanonicalDensityMatrix

2.7.3ThermodynamicQuantities

2.7.4TheGrandPartitionFunctionfortheClassicalIdealGas

*2.7.5TheGrandCanonicalDensityMatrixinSecondQuantization

Problems

3.Thermodynamics

3.1PotentialsandLaWSofEquilibriumThermodynamics

3.1.1Definitions

3.1.2TheLegendreTransformation

3.1.3TheGibbs-DuhemRelationinHomogeneousSystems

3.2DerivativesofThermodynamicQuantities

3.2.1Definitions

3.2.2IntegrabilityandtheMaxwellRelations

3.2.3Jacobians

3.2.4Examples

3.3FluctuationsandThermodynamicInequalities.

3.3.1Fluctuations

3.3.2Inequalities

3.4AbsoluteTemperatureandEmpiricalTemperatures

3.5ThermodynamicProcesses

3.5.1ThermodynamicConcepts

3.5.2TheIrreversibleExpansionofaGastheGay-LussacExperiment

3.5.3TheStatisticalFoundationofIrreversibility

3.5.4ReversibleProcesses

3.5.5TheAdiabaticEquation

……

3.Thermodynamics

4.IdealQuantumGases

5.RealGases,Liquids,andSolutions

6.Magnetism

7.PhaseTransitions,RenormalizationGroupTheroy,andPercolation

8.BrownianMotion,EquationsofMotionandtheFokker-PlanckEquations

9.TheBoltzmannEquation

10.IrreversibiltyandtheApproachtoEquilibrium

Appendix

SubjectIndex

　　“国外物理名著系列”具有权威性、前瞻性和应用性强的特点。本书为其中一册，包括平衡和非平衡统计物理的基本理论。除了在微正则密度矩阵单一假设下的平衡统计和热力学的演绎推理外，本书还重点论述了非平衡统计中的一些重要的原理。适用于掌握基本的量子力学知识的读者，可供物理学和相关理工科专业的高年级学生阅读参考。　　本书是经典的《统计力学》的修订版，包括平衡和非平衡统计物理的基本理论。除了在微正则密度矩阵单一假设下的平衡统计和热力学的演绎推理外，本书还重点论述了非平衡统计中的一些重要的原理。书中的计算都提供了详细的推导过程，每章后面附有习题，可以帮助学生巩固他们对教材的理解。除基础知识外，本书还论述了本领域的普适性及其应用的多样性，还包括一些新的领域，如重正化群，逾渗，运动的随机方程及其在临界动力学中的应用，动理学理论等，同时还讨论了不可逆论的基本原理。本书适用于掌握基本的量子力学知识的读者，可供物理学和相关理工科专业的高年级学生阅读参考。