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统计物理学 第1分册(第3版)(理论物理学教程 第5卷)作者:LDLandau,分类:文学 人气: 装帧:平装 / 24开 / 544页 / 0字 ISBN(10位/13位):7506242591 出版:世界图书出版公司于1999-05- 1出版 定价:¥75元 标签(Tags): 收藏人数： |
| 简介: |
| 片断： Theimportanceofstatisticalphysicsinmanyotherbranchesoftheoretical physicsisduetothefactthatinNaturewecontinuallyencountermacroscop- icbodieswhosebehaviourcannotbefullydescribedbythemethodsof mechanicsalone,forthereasonsmentionedabove,andwhichobeystatistical laws. Inproceedingtoformulatethefundamentalproblemofclassicalstatistics, wemustfirstofalldefinetheconceptofphasespace,whichwillbeconstantly usedhereafter. Letagivenmacroscopicmechanicalsystemhavesdegreesoffreedom |
| 目录: |
| CONTENTS Preface to the third Russian edition From the prefaces to previous Russian editions Nolation I. THE FUNDAMENTAL PRINCIPLES OF STATISTICAL PHYSICS 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 incrcase ofentropy 11. THERMODYNAMIC QUANTITIES 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 therrnodynamic 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 extemal medium 21. Thermodynamic inequalities 22. Le Chatelier's principle 23. Nemst's theorem 24. The dependence of the thermodynamic quantities on the number of particles 25. Equilibrium of a body in an extemal field 26. Rotating bodies 27. Thermodynamic relations in the relativistic region 111. THE GIBBS DISTRIBUTION 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 fi 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 IV. IDEAL GASES 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 moleculcs 49. Diatomic gases. Vibrations of atoms 50. Diatomic gases. The effect of the electronic angular momentum 51. Polyatomic gases 52. Magnetism of gases V. THE FERMl AND BOSE DISTRIBUTIONS 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 Vl SOLIDS 64. Solids at low temperatures 65. Solids at high temperatures 66. Debye's interpolation formula 67. Thennal 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 VII. NON-IDEAL GASES 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 coefflcient and the scattering amplitude 78. Thermodynamic quantities for a classical plasma ?79. The method of correlation functions 80. Thermodynamic quantities for a degenerate plasma VIII. PHASE EQUILIBRIUM ?81. Conditions of phase equilibrium ?82. The Clapeyron-Clausius fonnula ?83. The critical point ?84. The law of corresponding states IX. SOLUTIONS ?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 ofideal gases ?94. Mixtures of isotopes ?95. Vapour pressure over concentrated solutions ?96. Thennodynamic inequalities for solutions ?97. Equilibrium curves ?98. Examples of phase diagrams ?99. Intersection of singular curves on the cquilibrium surface ?100. Gases and liquids X CHEMICAL REACTIONS ?101. The condition for chemical equilibrium ?102. The law of mass action ?103. Heat ofreaction ?104. lonisation equilibrium ?105. Equilibrium with respect to pair production XI PROPERTIES OF MATTER AT VERY HIGH DENSITY ?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 XII. FLUCTUATIONS ?110. The Gaussian distribution ?111. The Gaussian distribution for more than one variable ?112. Fluctuations of the fundamental thennodynamic 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 fonn of the generalised susceptibility ?127. Fluctuations in the curvature of long molecules XIII. THE SYMMETRY OF CRYSTAL.S ?128. Symmetry elements of a crystal lattice ?129. The Bravais lattice ?130. Crystal systems 131. Crystal classes ?132. Spacegroups ?133. The reciprocal lattice ?134. Irreducible representations ofspace 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 XIV. PHASE TRANSITIONS OF THE SECOND KIND AND CRITICAL PHENOMENA ?142. Phase transitions of the second kind ?143. The discontinuity of specific heat ?144. Effect of an extemal 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 ofcontinuous 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 XV. SURFACES ?154. Surface tension ?155. Surface tension ofcrystals ?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-dimensiona! systems |
| 内容摘要: |
| The importance ofstatistical physics in many other branches of theoretical physics is due to the fact that in Nature we continually encounter macroscop- ic bodies whose behaviour can not be fully described by the methods of mechanics alone, for the reasons mentioned above, and which obey statistical laws. In proceeding to formulatethe fundamental problem ofclassical statistics, we must first ofall define the concept ofphase space, which will be constantly used hereafter. Let a given macroscopic mechanical system have s degrees of freedom: that is, let the position of points of the system in space be described by s co- ordinates, which we denote by q, the suffix i taking the values 1, 2, ..., s. Then the state of the system at a given instant will be defined by the values at that instant of the s coordinates q, and the s corresponding velocities q,. In statistics it is customary to describe a system by its coordinates and momenta p,, not velocities, since tbis affords a number ofvery important advantages. The various states ofthe system can be represented mathematically by points in phase space (which is, ofcourse, a purely mathematical concept); the co- ordinates in phase space are the coordinates and momenta ofthe system con- sidered. Every system has its own phase space, with a number of dimensions equa) to twice the number ofdegrees offreedom. Any point in phase space, corresponding to particular values of the coordinates q, and momenta p of the system, represents a particular state ofthe system. The state ofthesystem changes with time, and consequently the point in phase space representing this state (which we shall call simply the phase point of the system) moves along a curve called thephase trajectory. Let us now consider a macroscopic body or system of bodies, aod assume that the system is closed, i.e. does not interact with any other bodies. A part of the system, which is very small compared with the whole system but still macroscopic, may be imagined to be separated from the rest; clearly, when the number ofparticles in the whole system is sufficiently large, tbe number in a small part of it may still be very large. Such relatively small but still macroscopic parts will be called subsystems. A subsystem is again a mechani- cal system, but not a closed one; on the contrary, it interacts in various ways with the other parts ofthe system. Because ofthe very large number of degrees offreedom ofthe other parts, these interactions will be very complex and intricate. Thus the state of the subsystem considered will vary with time in a very complex and intricate manner. An exact solution for the behaviour ofthe subsystem can be obtained only by solving the mechanical problem for the entire closed system, i.e. by setting up and solving all the differential equations of motion with given initial con- ditions, which, as already mentioned, is an impracticable task. Fortunately, it is just this very complicated manner ofvariation ofthe state ofsubsystems which, though rendering the methods of mechanics inapplicable, allows a different approach to the solution of the problem. A fundamental feature of this approach is the fact that, because of the extreme complexity of the external interactions with the other parts of the system, during a sufficiently long time the subsystem considered will be many times in every possible state. This may be more precisely formulated as follows. Let Ap Aq denote some small "volume" of the phase space of the subsystem, corresponding to coordinates q, and momenta p lying in short intervals Aq, and Ap We can say that, in a sufficiently long time T, the extremely intricate phase trajectory passes many times through each such volume ofphase space. Let be the part ofthe total time Tdurine which the subsystem was in the given volume ofphase space ApAq? When the total time T increases indefinitely, the ratio t/T tends to some limit (1.1) This quantity may clearly be regarded as the probability that, if the subsys- tem is observed at an arbitrary instant, it will be found in the given volume of phase space ApAq. On taking the limit of an infinitesimal phase volume dq dp = dq1 dq2... dq, dp1 dp2... dp, (1.2) we can define the probability dw of states represented by points in this vol- ume element, i.e. the probability that the coordinates q and momenta p, have values in given infinitesimal intervals between q,, p, and q dq,, p dpr This probability dw may be written where (, ..., p,, q, ..., q,) is a function of all the coordinates and momenta; we shall usually write for brevity (p, q) or even simply. The function g, which represents the "density" oftheprobabilitydistribution in phase space, is called the statistical distribution function, or simply the For brevity, we shall usually say, as is customary, that the system "is in thc volume p q of phase space", mearning that the system is in states represented by phase points in tbat volume. In what follows we shall always use the conventional notation dp and dq to denote thc products of the differentials of all the momenta and all the coordinates of the system respectively. |
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