Statistical Mechanics book cover

Statistical Mechanics

Statistical Mechanics explores the physical properties of matter based on the dynamic behavior of its microscopic constituents. After a historical introduction, this book presents chapters about thermodynamics, ensemble theory, simple gases theory, Ideal Bose and Fermi systems, statistical mechanics of interacting systems, phase transitions, and computer simulations. This edition includes new topics such as BoseEinstein condensation and degenerate Fermi gas behavior in ultracold atomic gases and chemical equilibrium. It also explains the correlation functions and scattering; fluctuationdissipation theorem and the dynamical structure factor; phase equilibrium and the Clausius-Clapeyron equation; and exact solutions of one-dimensional fluid models and two-dimensional Ising model on a finite lattice. New topics can be found in the appendices, including finite-size scaling behavior of Bose-Einstein condensates, a summary of thermodynamic assemblies and associated statistical ensembles, and pseudorandom number generators. Other chapters are dedicated to two new topics, the thermodynamics of the early universe and the Monte Carlo and molecular dynamics simulations. This book is invaluable to students and practitioners interested in statistical mechanics and physics.

Audience
Graduate and Advanced Undergraduate Students in Physics. Researchers in the field of Statisical Physics.

Paperback, 744 Pages

Published: February 2011

Imprint: Academic Press

ISBN: 978-0-12-382188-1

Reviews

  • "An excellent graduate-level text. The selection of topics is very complete and gives to the student a wide view of the applications of statistical mechanics. The set problems reinforce the theory exposed in the text, helping the student to master the material"--Francisco Cevantes
    "Making sense out of the world around us in one of the most appealing facets of physics. One may start by putting together seemingly isolated observations and as the different pieces start to fall into place, more complicated arrangements and more fundamental explanations are sought. This is indeed the case for instance when trying to understand the behaviour of a collection of particles. On the one hand, thermo- dynamics provides us with a satisfactory explanation of the macroscopic phenomena observed, however, in order to get to the core of the physical system it becomes necessary to take into account the microscopic constituents of the system as well as the fact that quantum mechanical effects are at play. This is the realm of statistical mechanics and the subject of one of the most widely recognised textbooks around the globe: Pathria’s Statistical Mechanics.…The original style of the book is kept, and the clarity of explanations and derivations is still there. I am convinced that this third edition of Statistical Mechanics will enable a number of new generations of physicists to gain a solid background of statistical physics and that can only be a good thing."--Contemporary Physics, pages 619-620


Contents


  • Preface to the Third Edition

    Preface to the Second Edition

    Preface to the First 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

        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 91

        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

        5.3. Examples

        5.4. Systems composed of indistinguishable particles

        5.5. The density matrix and the partition function of a system of free particles

        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

        6.6. 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

        8.3. 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

        10.4. General remarks on cluster expansions

        10.5. Exact treatment of the second virial coefficient

        10.6. Cluster expansion for a quantum-mechanical system

        10.7. Correlations and scattering

        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

        11.3. 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 n

        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

        13.2. 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

        14.3. The renormalization group: general formulation

        14.4. Applications of the renormalization group

        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

        15.7. The Onsager relations

        Problems

    16. Computer Simulations

        16.1. Introduction and statistics

        16.2. Monte Carlo simulations

        16.3. Molecular dynamics

        16.4. Particle simulations

        16.5. Computer simulation caveats

        Problems

    Appendices

        A. Influence of boundary conditions on the distribution of quantum states

        B. Certain mathematical functions

        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

        I. Pseudorandom numbers

    Bibliography

    Index




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