A modern course in statistical physics

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1. Verfasser:	Reichl, Linda E. 1942- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Weinheim Wiley-VCH 2004
Ausgabe:	2. ed., [Nachdr.]
Schlagworte:	Thermodynamik Statistische Mechanik Statistische Thermodynamik Statistische Physik Lehrbuch
Online-Zugang:	Inhaltsverzeichnis
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Datensatz im Suchindex

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adam_text	CONTENTS Preface xix 1. Introduction 1 I.A. Overview 1 1.В. Plan of Book 2 l.C. Use as a Textbook 5 PART ONE THERMODYNAMICS 2. Introduction to Thermodynamics 9 2.A. Introductory Remarks 9 11 16 16 17 18 19 19 20 20 21 21 22 22 23 31 33 36 37 40 42 45 48 vii 2.B. State Variables and Exact Differentials 2.C. Some Mechanical Equations of State 2.С.1. Ideal Gas Law 2.C.2. Virial Expansion 2.C.3. Van der Waals Equation of State 2.C.4. Solids 2.C.5. Elastic Wire or Rod 2.C.6. Surface Tension 2.C.7. Electric Polarization 2.C.8. Curie s Law 2.D. The Laws of Thermodynamics 2.D.I. Zeroth Law 2.D.2. First Law 2.D.3. Second Law 2.D.4. Third Law 2.E. Fundamental Equation of Thermodynamics 2.F. Thermodynamic Potentials 2.F.I. Internal Energy 2.F.2. Enthalpy 2.F.3. Helmholz Free Energy 2.F.4. Gibbs Free Energy 2.F.5. Grand Potential iii CONTENTS 2.G. Response Functions 50 2.G.I. Thermal Response Functions (Heat Capacity) 50 2.G.2. Mechanical Response Functions 53 2.H. Stability of the Equilibrium State 55 2.Н.1. Conditions for Local Equilibrium in a PVT System 55 2.H.2. Conditions for Local Stability in a PVT System 57 2.H.3. Implications of the Stability Requirements for the Free Energies 63 S2.A. Cooling and Liquefactions of Gases 66 S2.A.1. The Joule Effect: Free Expansion 66 S2.A.2. The Joule-Kelvin Effect: Throttling 68 S2.B. Entropy of Mixing and the Gibbs Paradox 72 S2.C. Osmotic Pressure in Dilute Solutions 74 S2.D. The Thermodynamics of Chemical Reactions 78 S2.D.1. The Affinity 78 S2.D.2. Stability 82 S2.E. The Thermodynamics of Electrolytes 86 References 89 Problems 90 3. The Thermodynamics of Phase Transitions 96 ЗА. Introductory Remarks 96 3.B. Coexistence of Phases: Gibbs Phase Rule 98 3.C. Classification of Phase Transitions 100 3.D. Pure PVT Systems 103 3.ΌΛ. Phase Diagrams 103 3.D.2. Coexistence Curves: Clausius-Clapyron Equation 105 3.D.3. Liquid-Vapor Coexistence Region 110 3.D.4. The van der Waals Equation 115 3.E. Superconductors 118 3.F. The Helium Liquids 123 3.F.I. Liquid He4 123 3.F.2. Liquid He3 124 3.F.3. Liquid He3-He4 Mixtures 126 3.G. Landau Theory 128 3 .G. 1. Continuous Phase Transitions 128 3.G.2. First-Order Transitions 134 CONTENTS ix З.Н. Critical Exponents 135 З.Н.1. Definition of Critical Exponents 136 3.H.2. The Critical Exponents for Pure PVT Systems 137 S3.A. Surface Tension 142 S3.B. Thermomechanical Effect 146 S3.C. The Critical Exponents for the Curie Point 149 S3.D. Tricritical Points 151 S3.E. Binary Mixtures 153 S3.E.1. Stability Conditions 154 S3.E.2. Equilibrium Conditions 155 S3.E.3. Coexistence Curve 160 S3.F. The Ginzburg-Landau Theory of Superconductors 162 References 166 Problems 167 PART TWO CONCEPTS FROM PROBABILITY THEORY 4. Elementary Probability Theory and Limit Theorems 173 4.A. Introduction 173 4.B. Permutations and Combinations 174 4.C. Definition of Probability 175 4.D. Stochastic Variables and Probability 177 4.D.I. Distribution Functions 178 4.D.2. Moments 180 4.D.3. Characteristic Functions 182 4.D.4. Jointly Distributed Stochastic Variables 183 4.E. Binomial Distributions 188 4.Е.1. The Binomial Distribution 188 4.E.2. The Gaussian (For Normal) Distribution 191 4.E.3. The Poisson Distribution 192 4.E.4. Binomial Random Walk 194 4.F. A Central Limit Theorem and Law of Large Numbers 197 4.F.I. A Central Limit Theorem 197 4.F.2. The Law of Large Numbers 198 S4.A. Lattice Random Walk 199 S4.A.1. One-Dimensional Lattice 200 S4.A.2. Random Walk in Higher Dimension 203 x CONTENTS S4.B. Infinitely Divisible Distributions 207 S4.B.1. Gaussian Distribution 208 S4.B.2. Poisson Distribution 209 S4.B.3. Cauchy Distribution 209 S4.B.4. Levy Distribution 210 S4.C. The Central Limit Theorem 211 S4.C. 1. Useful Inequalities 212 S4.C.2. Convergence to a Gaussian 213 S4.D. Weierstrass Random Walk 214 S4.D.1. Discrete One-Dimensional Random Walk 215 S4.D.2. Continuum Limit of One-Dimensional Discrete Random Walk 217 S4.D.3. Two-Dimensional Discrete Random Walk (Levy Flight) 218 S4.E. General Form of Infinitely Divisible Distributions 221 S4.E.1. Levy-Khintchine Formula 222 S4.E.2. Kolmogorov Formula 223 References 225 Problems 225 5. Stochastic Dynamics and Brownian Motion 229 5.A. Introduction 229 5.B. General Theory 231 5.C. Markov Chains 234 5.С.1. Spectral Properties 234 5.C.2. Random Walk 240 5.D. The Master Equation 241 5.D.I. Derivation of the Master Equation 242 5.D.2. Detailed Balance 244 5.D.3. Mean First Passage Time 247 5.E. Brownian Motion 250 5.Е.1. Langevin Equation 251 5.E.2. The Spectral Density (Power Spectrum) 254 S5.A. Time Periodic Markov Chain 258 S5.B. Master Equation for Birth-Death Processes 260 SS-B.l. The Master Equation 260 853.2. Linear Birth-Death Processes 261 S5.B.3. Nonlinear Birth-Death Processes 265 CONTENTS xi Ѕб.С. The Fokker-Planck Equation 266 SS.C.l. Probability Flow in Phase Space 266 85.0.2. Probability Flow for Brownian Particle 267 S5.C3. The Strong Friction Limit 270 S5.C.4. Solution of Fokker-Planck Equations with One Variable 271 S5.D. Approximations to the Master Equation 276 References 278 Problems 279 6. The Foundations of Statistical Mechanics 285 6.A. Introduction 285 6.B. The Liouville Equation of Motion 286 6.C. Ergodic Theory and the Foundation of Statistical Mechanics 296 6.D. The Quantum Probability Density Operator 303 S6.A. Reduced Probability Densities and the BBGKY ffierarchy 310 S6.B. Reduced Density Matrices and the Wigner Distribution 314 S6.C. Microscopic Balance Equations 319 S6.D. Mixing Flow 321 S6.E. Anharmonic Oscillator Systems 326 S6.F. Newtonian Dynamics and Irreversibility 334 References 335 Problems 336 PART THREE EQUILIBRIUM STATISTICAL MECHANICS 7. Equilibrium Statistical Mechanics 341 7.A. Introduction 341 7.B. The Microcanonical Ensemble 343 7.C. Einstein Fluctuation Theory 349 7.С.1. General Discussion 349 7.C.2. Fluid Systems 351 7.D. The Canonical Ensemble 354 7.D.I. Probability Density Operator 354 7.D.2. Systems of Indistinguishable Particles 357 7.D.3. Systems of Distinguishable Particles 362 7.E. Heat Capacity of a Debye Solid 364 xii CONTENTS 7.F. Order-Disorder Transitions 369 7.F.I. Exact Solution for a One-Dimensional Lattice 370 7.F.2. Mean Field Theory for a d-Dimensional Lattice 372 7.G. The Grand Canonical Ensemble 377 7.H. Ideal Quantum Gases 381 7.Н.1. Bose-Einstein Gases 383 7.H.2. Fermi-Dirac Ideal Gases 392 S7.A. Heat Capacity of Lattice Vibrations on a One- Dimensional Lattice — Exact Solution 401 S7.A.1. Exact Expression — Large N 404 S7.A.2. Continuum Approximation — Large N 406 S7.B. Momentum Condensation in an Interacting Fermi Fluid 407 S7.C. The Yang-Lee Theory of Phase Transitions 418 References 422 Problems 423 8. Order-Disorder Transitions and Renormalizatíon Theory 427 8-А. Introduction 427 8.B. Static Correlation Functions and Response Functions 428 8.В.1. General Relations 429 8.B.2. Application to the Ising Lattice 431 8.C. Scaling 433 8.С.1. Homogeneous Functions 433 8.C.2. Widom Scaling 434 8.C.3. Kadanoff Scaling 437 8.D. Microscopic Calculation of Critical Exponents 440 S8.A. Critical Exponents for the S4 Model 448 S8.B. Exact Solution of the Two-Dimensional Ising Model 462 S8.B.1. Partition Function 462 S8.B.2. Antisymmetric Matrices and Dimer Graphs 466 S8.B.3. Closed Graphs and Mixed Dimer Graphs 469 S8.B.4. Partition Function for Infinite Planar Lattice 475 References 485 Problems 486 9. Interacting Fluids 488 9.A. Introduction 488 9.B. Thermodynamics and the Radial Distribution Function 489 CONTENTS xiii 9.C. Vinal Expansion of the Equation of State 492 9.С.1. Vinal Expansions and Cluster Functions 493 9.C.2. The Second Virial Coefficient 500 9.C.3. Higher-Order Virial Coefficients 506 S9.A. The Pressure and Compressibility Equations 507 S9.A.1. The Pressure Equation 508 S9.A.2. The Compressibility Equation 509 S9.B. Ornstein-Zernicke Equation 510 S9.C. Third Virial Coefficient 513 S9.C.1. Square-Well Potential 514 S9.C.2. Lennard-Jones 6-12 Potential 515 S9.D. Virial Coefficients for Quantum Gases 517 References 526 Problems 527 PART FOUR NONEQUILIBRIUM STATISTICAL MECHANICS 10. Hydrodynamic Processes Near Equilibrium 531 10.A. Introduction 531 10.B. Navier-Stokes Hydrodynamic Equations 533 10.B.1. Balance Equations 534 10.B.2. Entropy Source and Entropy Current 537 10.B.3. Transport Coefficients 541 10.C. Linearized Hydrodynamic Equations 544 lO.C.l. Linearization of the Hydrodynamic Equations 545 10.C.2. Transverse Hydrodynamic Modes 549 10.C.3. Longitudinal Hydrodynamic Modes 550 10.D. Dynamic Equilibrium Fluctuations and Transport Processes 552 10.D.1. Onsager s Relations 553 10.D.2. Weiner-Khintchine Theorem 557 10.E. Linear Response Theory and the Fluctuation-Dissipation Theorem 561 10.E.1. The Response Matrix 562 10.E.2. Causality 563 10.E.3. The Fluctuation-Dissipation Theorem 568 10.E.4. Power Absorption 570 10.F. Transport Properties of Mixtures 574 lO.F.l. Entropy Production in Multicomponent Systems 574 xiv CONTENTS ÏO.F.L Fick s Law for Diffusion 580 10.F.3. Thermal Diffusion 582 10.F.4. Electrical Conductivity and Diffusion in Fluids 583 S 10. A. Onsager s Relations When a Magnetic Field is Present 586 S10.B. Microscopic Linear Response Theory 589 S10.C. Light Scattering 592 SlO.C.l. Scattered Electric Field 594 SIO.C^. Intensity of Scattered Light 597 S10.D. Thermoelectricity 600 S10.D.1. The Peltier Effect 601 S10.D.2. The Seebeck Effect 603 S10.D.3. Thomson Heat 605 SI O.E. Entropy Production in Discontinuous Systems 605 SI O.E.I. Volume Flow Across a Membrane 606 S10.E.2. Ion Transport Across a Membrane 610 S10.F. Stochastic Hydrodynamics 612 S10.F.1. Stochastic Hydrodynamic Equations 613 S10.F.2. Properties of Equilibrium Correlation Functions 614 S10.F.3. Random Current Correlation Functions 617 S10.G. Long-Time Tails 620 S10.G.1. Fluid Flow Around the Brownian Particle 621 S10.G.2. Drag Force on the Brownian Particle 623 S10.G.3. Velocity Autocorrelation Function 624 S10.H. Superfluid Hydrodynamics 631 SI O.H.I. Superfluid Hydrodynamic Equations 631 S10.H.2. Sound Modes 635 SI 0.1. General Definition of Hydrodynamic Modes 639 510.1.1. Projection Operators 640 510.1.2. Conserved Quantities 642 S 10.I.3. Hydrodynamic Modes Due to Broken Symmetry 644 References 649 Problems 650 11. Transport Theory 656 H.A. Introduction 656 ll.B. Elementary Transport Theory 657 11 .B.I . The Maxwell-Boltzmann Distribution 657 11.B.2. The Mean Free Path 658 CONTENTS xv П.В.З. The Collision Frequency 659 11. В .4. Self-Diffusion 661 П-В-б. The Coefficients of Viscosity and Thermal Conductivity 664 11.B.6. The Rate of Reaction 666 U.C. The Boltzmann Equation 670 11 .C. 1. Two-Body Scattering 671 H.C.2. Derivation of the Boltzmann Equation 679 11.C.3. Boltzmann s H Theorem 680 ll.D. Linearized Boltzmann and Lorentz-Boltzmann Equations 682 11.D.I. Kinetic Equations for a Two-Component Gas 682 11.D.2. Collision Operators 684 U.E. Coefficient of Self-Diffusion 688 11. E.I. Derivation of the Diffusion Equation 688 11.E.2. Eigenfrequencies of the Lorentz- Boltzmann Equation 690 11.F. Coefficients of Viscosity and Thermal Conductivity 691 11. F.I. Derivation of the Hydrodynamic Equations 692 1 l.F.2. Eigenfrequencies of the Boltzmann Equation 697 11.F.3. Shear Viscosity and Thermal Conductivity 700 ll.G. Computation of Transport Coefficients 701 11. G.I. Sonine Polynomials 702 11.0.2. Diffusion Coefficient 703 11.G.3. Thermal Conductivity 704 11.G.4. Shear Viscosity 708 S 11. A. Beyond the Boltzmann Equation 710 References 717 Problems 718 12. Nonequilibrium Phase Transitions 721 12. A. Introduction 721 12.B. Nonequilibrium Stability Criteria 722 12.B.1. Stability Conditions Near Equilibrium 723 12.B.2. Stability Conditions Far From Equilibrium 726 12.C. The Schlogl Model 732 12.D. The Brasselator 735 12.D.1. The Brusselator — A Nonlinear Chemical Model 736 12.D.2. Boundary Conditions 737 xvi CONTENTS 12.D.3. Linear Stability Analysis 739 12.E. The Rayleigh-Bénard Instability 742 И.ЕЛ. Hydrodynamic Equations and Boundary Conditions 743 12.E.2. Linear Stability Analysis 747 S 12. A. Fluctuations Near a Nonequilibrium Phase Transition 753 S12.A.1. Fluctuations in the Rayleigh-Bénard System 753 S12.A.2. Fluctuations in the Brusselator 760 S12.A.3. The Time-Dependent Ginzburg-Landau Equation 764 References 765 Problems 767 APPENDICES A. Balance Equations 768 A.I. General Fluid Flow 768 A.2. General Balance Equation 771 References 773 B. Systems of Identical Particles 774 B.I. Position and Momentum Eigenstates 774 B.I.I. Free Particle 775 B.I. 2. Particle in a Box 776 B.2. Symmetrized iV-Particle Position and Momentum Eigenstates 777 B.2.1. Symmetrized Momentum Eigenstates for Bose-Einstein Particles 778 B.2.2. Antisymmetrized Momentum Eigenstates for Fermi-Dirac Particles 779 B.2.3. Partition Functions and Expectation Values 780 B.3. The Number Representation 781 B.3.1. The Number Representation for Bosons 782 B.3.2. The Number Representation for Fermions 785 B.3.3. Field Operators 788 References 790 C. Stability of Solutions to Nonlinear Equations 791 C.I. Linear Stability Theory 791 CONTENTS xvii C.2. Limit Cycles 795 С.З. Liapounov Functions and Global Stability 796 References 798 Author Index 799 Subject Index 804
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owner	DE-703 DE-19 DE-BY-UBM DE-29T DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-11
owner_facet	DE-703 DE-19 DE-BY-UBM DE-29T DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-11
physical	XIX, 822 S. Ill., graph. Darst.
publishDate	2004
publishDateSearch	2004
publishDateSort	2004
publisher	Wiley-VCH
record_format	marc
spellingShingle	Reichl, Linda E. 1942- A modern course in statistical physics Thermodynamik (DE-588)4059827-5 gnd Statistische Mechanik (DE-588)4056999-8 gnd Statistische Thermodynamik (DE-588)4126251-7 gnd Statistische Physik (DE-588)4057000-9 gnd
subject_GND	(DE-588)4059827-5 (DE-588)4056999-8 (DE-588)4126251-7 (DE-588)4057000-9 (DE-588)4123623-3
title	A modern course in statistical physics
title_auth	A modern course in statistical physics
title_exact_search	A modern course in statistical physics
title_full	A modern course in statistical physics L. E. Reichl
title_fullStr	A modern course in statistical physics L. E. Reichl
title_full_unstemmed	A modern course in statistical physics L. E. Reichl
title_short	A modern course in statistical physics
title_sort	a modern course in statistical physics
topic	Thermodynamik (DE-588)4059827-5 gnd Statistische Mechanik (DE-588)4056999-8 gnd Statistische Thermodynamik (DE-588)4126251-7 gnd Statistische Physik (DE-588)4057000-9 gnd
topic_facet	Thermodynamik Statistische Mechanik Statistische Thermodynamik Statistische Physik Lehrbuch
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014577754&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT reichllindae amoderncourseinstatisticalphysics

A modern course in statistical physics

MARC

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