Statistical Physics, Volume 5 by Landau, L.D. -- Read -- Imperial Library of Trantor

Index

Cover image Title page Table of Contents Other tities in the COURSE OF THEORETICAL PHYSICS Copyright PREFACE TO THE THIRD RUSSIAN EDITION FROM THE PREFACES TO PREVIOUS RUSSIAN EDITIONS NOTATION CONTENTS OF PART 2 Chapter 1: THE FUNDAMENTAL PRINCIPLES OF STATISTICAL PHYSICS

Publisher Summary § 1 Statistical distributions § 2 Statistical independence § 3 Liouville’s theorem § 4 The significance of energy § 5 The statistical matrix § 6 Statistical distributions in quantum statistics § 7 Entropy § 8 The law of increase of entropy

Chapter 2: THERMODYNAMIC QUANTITIES

Publisher Summary § 9 Temperature § 10 Macroscopic motion § 11 Adiabatic processes § 12 Pressure § 13 Work and quantity of heat § 14 The heat function § 15 The free energy and the thermodynamic potential § 16 Relations between the derivatives of thermodynamic quantities § 17 The thermodynamic scale of temperature § 18 The Joule-Thomson process § 19 Maximum work § 20 Maximum work done by a body in an external medium § 21 Thermodynamic inequalities § 22 Le Chatelier’s principle § 23 Nernst’s theorem § 24 The dependence of the thermodynamic quantities on the number of particles § 25 Equilibrium of a body in an external field § 26 Rotating bodies § 27 Thermodynamic relations in the relativistic region

Chapter 3: THE GIBBS DISTRIBUTION

Publisher Summary § 28 The Gibbs distribution § 29 The Maxwellian distribution § 30 The probability distribution for an oscillator § 31 The free energy in the Gibbs distribution § 32 Thermodynamic perturbation theory § 33 Expansion in powers of § 34 The Gibbs distribution for rotating bodies § 35 The Gibbs distribution for a variable number of particles § 36 The derivation of the thermodynamic relations from the Gibbs distribution

Chapter 4: IDEAL GASES

Publisher Summary § 37 The Boltzmann distribution § 38 The Boltzmann distribution in classical statistics § 39 Molecular collisions § 40 Ideal gases not in equilibrium § 41 The free energy of an ideal Boltzmann gas § 42 The equation of state of an ideal gas § 43 Ideal gases with constant specific heat § 44 The law of equipartition § 45 Monatomic ideal gases § 46 Monatomic gases. The effect of the electronic angular momentum § 47 Diatomic gases with molecules of unlike atoms. Rotation of molecules § 48 Diatomic gases with molecules of like atoms. Rotation of molecules § 49 Diatomic gases. Vibrations of atoms § 50 Diatomic gases. The effect of the electronic angular momentum § 51 Polyatomic gases § 52 Magnetism of gases

Chapter 5: THE FERMI AND BOSE DISTRIBUTIONS

Publisher Summary § 53 The Fermi distribution § 54 The Bose distribution § 55 Fermi and Bose gases not in equilibrium § 56 Fermi and Bose gases of elementary particles § 57 A degenerate electron gas § 58 The specific heat of a degenerate electron gas § 59 Magnetism of an electron gas. Weak fields § 60 Magnetism of an electron gas. Strong fields § 61 A relativistic degenerate electron gas § 62 A degenerate Bose gas § 63 Black-body radiation

Chapter 6: SOLIDS

Publisher Summary § 64 Solids at low temperatures § 65 Solids at high temperatures § 66 Debye’s interpolation formula § 67 Thermal expansion of solids § 68 Highly anisotropic crystals § 69 Crystal lattice vibrations § 70 Number density of vibrations § 71 Phonons § 72 Phonon creation and annihilation operators § 73 Negative temperatures

Chapter 7: NON-IDEAL GASES

Publisher Summary § 74 Deviations of gases from the ideal state § 75 Expansion in powers of the density § 76 Van der Waals’ formula § 77 Relationship of the virial coefficient and the scattering amplitude § 78 Thermodynamic quantities for a classical plasma § 79 The method of correlation functions § 80 Thermodynamic quantities for a degenerate plasma

Chapter 8: PHASE EQUILIBRIUM

Publisher Summary § 81 Conditions of phase equilibrium § 82 The Clapeyron-Clausius formula § 83 The critical point § 84 The law of corresponding states

Chapter 9: SOLUTIONS

Publisher Summary § 85 Systems containing different particles § 86 The phase rule § 87 Weak solutions § 88 Osmotic pressure § 89 Solvent phases in contact § 90 Equilibrium with respect to the solute § 91 Evolution of heat and change of volume on dissolution § 92 Solutions of strong electrolytes § 93 Mixtures of ideal gases § 94 Mixtures of isotopes § 95 Vapour pressure over concentrated solutions § 96 Thermodynamic inequalities for solutions § 97 Equilibrium curves § 98 Examples of phase diagrams § 99 Intersection of singular curves on the equilibrium surface § 100 Gases and liquids

Chapter 10: CHEMICAL REACTIONS

Publisher Summary § 101 The condition for chemical equilibrium § 102 The law of mass action § 103 Heat of reaction § 104 Ionisation equilibrium § 105 Equilibrium with respect to pair production

Chapter 11: PROPERTIES OF MATTER AT VERY HIGH DENSITY

Publisher Summary § 106 The equation of state of matter at high density § 107 Equilibrium of bodies of large mass § 108 The energy of a gravitating body § 109 Equilibrium of a neutron sphere

Chapter 12: FLUCTUATIONS

Publisher Summary § 110 The Gaussian distribution § 111 The Gaussian distribution for more than one variable § 112 Fluctuations of the fundamental thermodynamic quantities § 113 Fluctuations in an ideal gas § 114 Poisson’s formula § 115 Fluctuations in solutions § 116 Spatial correlation of density fluctuations § 117 Correlation of density fluctuations in a degenerate gas § 118 Correlations of fluctuations in time § 119 Time correlations of the fluctuations of more than one variable § 120 The symmetry of the kinetic coefficients § 121 The dissipative function § 122 Spectral resolution of fluctuations § 123 The generalised susceptibility § 124 The fluctuation-dissipation theorem § 125 The fluctuation-dissipation theorem for more than one variable § 126 The operator form of the generalised susceptibility § 127 Fluctuations in the curvature of long molecules

Chapter 13: THE SYMMETRY OF CRYSTALS

Publisher Summary § 128 Symmetry elements of a crystal lattice § 129 The Bravais lattice § 130 Crystal systems § 131 Crystal classes § 132 Space groups § 133 The reciprocal lattice § 134 Irreducible representations of space groups § 135 Symmetry under time reversal § 136 Symmetry properties of normal vibrations of a crystal lattice § 137 Structures periodic in one and two dimensions § 138 The correlation function in two-dimensional systems § 139 Symmetry with respect to orientation of molecules § 140 Nematic and cholesteric liquid crystals § 141 Fluctuations in liquid crystals

Chapter 14: PHASE TRANSITIONS OF THE SECOND KIND AND CRITICAL PHENOMENA

Publisher Summary § 142 Phase transitions of the second kind § 143 The discontinuity of specific heat § 144 Effect of an external field on a phase transition § 145 Change in symmetry in a phase transition of the second kind § 146 Fluctuations of the order parameter § 147 The effective Hamiltonian § 148 Critical indices § 149 Scale invariance § 150 Isolated and critical points of continuous transition § 151 Phase transitions of the second kind in a two-dimensional lattice § 152 Van der Waals theory of the critical point § 153 Fluctuation theory of the critical point

Chapter 15: SURFACES

Publisher Summary § 154 Surface tension § 155 Surface tension of crystals § 156 Surface pressure § 157 Surface tension of solutions § 158 Surface tension of solutions of strong electrolytes § 159 Adsorption § 160 Wetting § 161 The angle of contact § 162 Nucleation in phase transitions § 163 The impossibility of the existence of phases in one-dimensional systems

INDEX