# Statistical Mechanics

## 3rd Edition

**Authors:**R K Pathria Paul D. Beale

**Print ISBN:**9780123821881

**eBook ISBN:**9780123821898

**Imprint:**Academic Press

**Published Date:**28th February 2011

**Page Count:**744

## Description

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.

## Key Features

-Bose-Einstein condensation in atomic gases

-Thermodynamics of the early universe

-Computer simulations: Monte Carlo and molecular dynamics

-Correlation functions and scattering

-Fluctuation-dissipation theorem and the dynamical structure factor

-Chemical equilibrium

-Exact solution of the two-dimensional Ising model for

finite systems

-Degenerate atomic Fermi gases

-Exact solutions of one-dimensional

fluid models

-Interactions in ultracold Bose and Fermi gases

-Brownian motion of anisotropic particles and harmonic oscillators

## Readership

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

## Table of Contents

Preface to the Third Edition

Preface to the Second Edition

Preface to the First Edition

Historical Introduction

Chapter 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

Chapter 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

Chapter 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

Chapter 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

## Details

- No. of pages:
- 744

- Language:
- English

- Copyright:
- © Academic Press 2011

- Published:
- 28th February 2011

- Imprint:
- Academic Press

- eBook ISBN:
- 9780123821898

- Paperback ISBN:
- 9780123821881

## About the Author

### R K Pathria

### Affiliations and Expertise

University of California at San Diego

### Paul D. Beale

### Affiliations and Expertise

University of Colorado at Boulder

## 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