Avenger

Statistical Mechanics, Fourth Edition, explores the physical properties of matter based on the dynamic behavior of its microscopic constituents. This valuable textbook introduces the reader to the historical context of the subject before delving deeper into chapters about thermodynamics, ensemble theory, simple gases theory, Ideal Bose and Fermi systems, statistical mechanics of interacting systems, phase transitions, and computer simulations. In the latest revision, the book's authors have updated the content throughout, including new coverage on biophysical applications, updated exercises, and computer simulations. This updated edition will be an indispensable to students and researchers of statistical mechanics, thermodynamics, and physics. Contents Preface to the first edition Preface to the second edition Preface to the third edition Preface to the fourth edition Historical introduction 1 The statistical basis of thermodynamics 1.1 The macroscopic and the microscopic states 1.2 Contact between statistics and thermodynamics: physical significance of the number Ω(N, V, E) 1.3 Further contact between statistics and thermodynamics 1.4 The classical ideal gas 1.5 The entropy of mixing and the Gibbs paradox 1.6 The ``correct'' enumeration of the microstates Problems 2 Elements of ensemble theory 2.1 Phase space of a classical system 2.2 Liouville's theorem and its consequences 2.3 The microcanonical ensemble 2.4 Examples 2.5 Quantum states and the phase space Problems 3 The canonical ensemble 3.1 Equilibrium between a system and a heat reservoir 3.2 A system in the canonical ensemble The method of most probable values The method of mean values 3.3 Physical significance of the various statistical quantities in the canonical ensemble 3.4 Alternative expressions for the partition function 3.5 The classical systems 3.6 Energy fluctuations in the canonical ensemble: correspondence with the microcanonical ensemble 3.7 Two theorems – the ``equipartition'' and the ``virial'' 3.8 A system of harmonic oscillators 3.9 The statistics of paramagnetism 3.10 Thermodynamics of magnetic systems: negative temperatures Problems 4 The grand canonical ensemble 4.1 Equilibrium between a system and a particle–energy reservoir 4.2 A system in the grand canonical ensemble 4.3 Physical significance of the various statistical quantities 4.4 Examples 4.5 Density and energy fluctuations in the grand canonical ensemble: correspondence with other ensembles 4.6 Thermodynamic phase diagrams 4.7 Phase equilibrium and the Clausius–Clapeyron equation Problems 5 Formulation of quantum statistics 5.1 Quantum-mechanical ensemble theory: the density matrix 5.2 Statistics of the various ensembles 5.2.A The microcanonical ensemble 5.2.B The canonical ensemble 5.2.C The grand canonical ensemble 5.3 Examples 5.3.A An electron in a magnetic field 5.3.B A free particle in a box 5.3.C A linear harmonic oscillator 5.4 Systems composed of indistinguishable particles 5.5 The density matrix and the partition function of a system of free particles 5.6 Eigenstate thermalization hypothesis Problems 6 The theory of simple gases 6.1 An ideal gas in a quantum-mechanical microcanonical ensemble 6.2 An ideal gas in other quantum-mechanical ensembles 6.3 Statistics of the occupation numbers 6.4 Kinetic considerations 6.5 Gaseous systems composed of molecules with internal motion 6.5.A Monatomic molecules 6.5.B Diatomic molecules 6.6 Chemical equilibrium Problems 7 Ideal Bose systems 7.1 Thermodynamic behavior of an ideal Bose gas 7.2 Bose–Einstein condensation in ultracold atomic gases 7.3 Thermodynamics of the blackbody radiation 7.4 The field of sound waves 7.5 Inertial density of the sound field 7.6 Elementary excitations in liquid helium II Problems 8 Ideal Fermi systems 8.1 Thermodynamic behavior of an ideal Fermi gas 8.2 Magnetic behavior of an ideal Fermi gas 8.2.A Pauli paramagnetism 8.2.B Landau diamagnetism 8.3 The electron gas in metals 8.4 Ultracold atomic Fermi gases 8.5 Statistical equilibrium of white dwarf stars 8.6 Statistical model of the atom Problems 9 Thermodynamics of the early universe 9.1 Observational evidence of the Big Bang 9.2 Evolution of the temperature of the universe 9.3 Relativistic electrons, positrons, and neutrinos 9.4 Neutron fraction 9.5 Annihilation of the positrons and electrons 9.6 Neutrino temperature 9.7 Primordial nucleosynthesis 9.8 Recombination 9.9 Epilogue Problems 10 Statistical mechanics of interacting systems: the method of cluster expansions 10.1 Cluster expansion for a classical gas 10.2 Virial expansion of the equation of state 10.3 Evaluation of the virial coefficients Problems 11 Statistical mechanics of interacting systems: the method of quantized fields 11.1 The formalism of second quantization 11.2 Low-temperature behavior of an imperfect Bose gas 11.2.A Effects of interactions on ultracold atomic Bose–Einstein condensates 11.3 Low-lying states of an imperfect Bose gas 11.4 Energy spectrum of a Bose liquid 11.5 States with quantized circulation 11.6 Quantized vortex rings and the breakdown of superfluidity 11.7 Low-lying states of an imperfect Fermi gas 11.8 Energy spectrum of a Fermi liquid: Landau's phenomenological theory 11.9 Condensation in Fermi systems Problems 12 Phase transitions: criticality, universality, and scaling 12.1 General remarks on the problem of condensation 12.2 Condensation of a van der Waals gas 12.3 A dynamical model of phase transitions 12.4 The lattice gas and the binary alloy 12.5 Ising model in the zeroth approximation 12.6 Ising model in the first approximation 12.7 The critical exponents 12.8 Thermodynamic inequalities 12.9 Landau's phenomenological theory 12.10 Scaling hypothesis for thermodynamic functions 12.11 The role of correlations and fluctuations 12.12 The critical exponents ν and η 12.13 A final look at the mean field theory Problems 13 Phase transitions: exact (or almost exact) results for various models 13.1 One-dimensional fluid models 13.1.A Hard spheres on a ring 13.2 The Ising model in one dimension 13.3 The n-vector models in one dimension 13.4 The Ising model in two dimensions 13.5 The spherical model in arbitrary dimensions 13.6 The ideal Bose gas in arbitrary dimensions 13.7 Other models Problems 14 Phase transitions: the renormalization group approach 14.1 The conceptual basis of scaling 14.2 Some simple examples of renormalization 14.2.A The Ising model in one dimension 14.3 The renormalization group: general formulation 14.4 Applications of the renormalization group 14.4.A The Ising model in one dimension 14.4.B The spherical model in one dimension 14.4.C The Ising model in two dimensions 14.5 Finite-size scaling Problems 15 Fluctuations and nonequilibrium statistical mechanics 15.1 Equilibrium thermodynamic fluctuations 15.2 The Einstein–Smoluchowski theory of the Brownian motion 15.3 The Langevin theory of the Brownian motion 15.4 Approach to equilibrium: the Fokker–Planck equation 15.5 Spectral analysis of fluctuations: the Wiener–Khintchine theorem 15.6 The fluctuation–dissipation theorem 15.6.A Derivation of the fluctuation–dissipation theorem from linear response theory 15.6.B Inelastic scattering 15.7 The Onsager relations 15.8 Exact equilibrium free energy differences from nonequilibrium measurements Problems 16 Computer simulations 16.1 Introduction and statistics 16.2 Monte Carlo simulations 16.2.A Metropolis Monte Carlo algorithm 16.3 Molecular dynamics 16.3.A Molecular dynamics algorithm 16.4 Particle simulations 16.4.A Simulations of hard spheres 16.5 Computer simulation caveats Problems Appendices A Influence of boundary conditions on the distribution of quantum states B Certain mathematical functions Stirling's formula for ν! The Dirac delta function C ``Volume'' and ``surface area'' of an n-dimensional sphere of radius R D On Bose–Einstein functions E On Fermi–Dirac functions F A rigorous analysis of the ideal Bose gas and the onset of Bose–Einstein condensation G On Watson functions H Thermodynamic relationships Entropy S(N,V,U) and the microcanonical ensemble Internal energy U(N,V,S) Helmholtz free energy A(N,V,T)=U-TS and the canonical ensemble Thermodynamic potential Π(μ,V,T)=-A + μN=P V and the grand canonical ensemble Gibbs free energy G(N,P,T)=A+PV=U-TS+PV=μN and the isobaric ensemble Enthalpy H(N,P,S)=U+PV Magnetic and electric free energy A(T,H,E)=U(S,M,P)-TS -μ0 HM - E P Convexity and variances I Pseudorandom numbers Gaussian-distributed pseudorandom numbers Bibliography Index This text is designed for postgraduate courses in statistical mechanics, and provides a basic grounding in a manner that brings out the essence of the subject with due rigour but without undue pain. This classic text, which was first published in 1972 and has continued to be popular ever since, has now been brought up to date by incorporating the remarkable developments in the field of phase transitions and critical phenomena that have taken place in the intervening years. This has been done by adding three new chapters which will enhance the usefulness of this book both for students and instructors. Widely acclaimed for its clean derivations and clear explanations, Statistical Mechanics in its second edition will continue to provide further generations of students with a solid training in the methods of statistical physics.