A concise introduction to statistical mechanicsStatistical mechanics is one of the most exciting areas of physics today, and it also has applications to subjects as diverse as economics, social behavior, algorithmic theory, and evolutionary biology. Statistical Mechanics in a Nutshell offers the most concise, self-contained introduction to this rapidly developing field. Requiring only a background in elementary calculus and elementary mechanics, this book starts with the basics, introduces the most important developments in classical statistical mechanics over the last thirty years, and guides readers to the very threshold of today's cutting-edge research.Statistical Mechanics in a Nutshell zeroes in on the most relevant and promising advances in the field, including the theory of phase transitions, generalized Brownian motion and stochastic dynamics, the methods underlying Monte Carlo simulations, complex systems-and much, much more. The essential resource on the subject, this book is the most up-to-date and accessible introduction available for graduate students and advanced undergraduates seeking a succinct primer on the core ideas of statistical mechanics.

Preface to the English Edition xiPreface xiiiChapter 1: Introduction 11.1 The Subject Matter of Statistical Mechanics 11.2 Statistical Postulates 31.3 An Example: The Ideal Gas 31.4 Conclusions 7Recommended Reading 8
Chapter 2: Thermodynamics 92.1 Thermodynamic Systems 92.2 Extensive Variables 112.3 The Central Problem of Thermodynamics 122.4 Entropy 132.5 Simple Problems 142.6 Heat and Work 182.7 The Fundamental Equation 232.8 Energy Scheme 242.9 Intensive Variables and Thermodynamic Potentials 262.10 Free Energy and Maxwell Relations 302.11 Gibbs Free Energy and Enthalpy 312.12 The Measure of Chemical Potential 332.13 The Koenig Born Diagram 352.14 Other Thermodynamic Potentials 362.15 The Euler and Gibbs-Duhem Equations 372.16 Magnetic Systems 392.17 Equations of State 402.18 Stability 412.19 Chemical Reactions 442.20 Phase Coexistence 452.21 The Clausius-Clapeyron Equation 472.22 The Coexistence Curve 482.23 Coexistence of Several Phases 492.24 The Critical Point 502.25 Planar Interfaces 51Recommended Reading 54
Chapter 3: The Fundamental Postulate 553.1 Phase Space 553.2 Observables 573.3 The Fundamental Postulate: Entropy as Phase-Space Volume 583.4 Liouville's Theorem 593.5 Quantum States 633.6 Systems in Contact 663.7 Variational Principle 673.8 The Ideal Gas 683.9 The Probability Distribution 703.10 Maxwell Distribution 713.11 The Ising Paramagnet 713.12 The Canonical Ensemble 743.13 Generalized Ensembles 773.14 The p-T Ensemble 803.15 The Grand Canonical Ensemble 823.16 The Gibbs Formula for the Entropy 843.17 Variational Derivation of the Ensembles 863.18 Fluctuations of Uncorrelated Particles 87Recommended Reading 88
Chapter 4: Interaction-Free Systems 894.1 Harmonic Oscillators 894.2 Photons and Phonons 934.3 Boson and Fermion Gases 1024.4 Einstein Condensation 1124.5 Adsorption 1144.6 Internal Degrees of Freedom 1164.7 Chemical Equilibria in Gases 123Recommended Reading 124
Chapter 5: Phase Transitions 1255.1 Liquid-Gas Coexistence and Critical Point 1255.2 Van der Waals Equation 1275.3. Other Singularities 1295.4 Binary Mixtures 1305.5 Lattice Gas 1315.6 Symmetry 1335.7 Symmetry Breaking 1345.8 The Order Parameter 1355.9 Peierls Argument 1375.10 The One-Dimensional Ising Model 1405.11 Duality 1425.12 Mean-Field Theory 1445.13 Variational Principle 1475.14 Correlation Functions 1505.15 The Landau Theory 1535.16 Critical Exponents 1565.17 The Einstein Theory of Fluctuations 1575.18 Ginzburg Criterion 1605.19 Universality and Scaling 1615.20 Partition Function of the Two-Dimensional Ising Model 165Recommended Reading 170
Chapter 6: Renormalization Group 1736.1 Block Transformation 1736.2 Decimation in the One-Dimensional Ising Model 1766.3 Two-Dimensional Ising Model 1796.4 Relevant and Irrelevant Operators 1836.5 Finite Lattice Method 1876.6 Renormalization in Fourier Space 1896.7 Quadratic Anisotropy and Crossover 2026.8 Critical Crossover 2036.9 Cubic Anisotrophy 2086.10 Limit n 2096.11 Lower and Upper Critical Dimensions 213Recommended Reading 214
Chapter 7: Classical Fluids 2157.1 Partition Function for a Classical Fluid 2157.2 Reduced Densities 2197.3 Virial Expansion 2277.4 Perturbation Theory 2447.5 Liquid Solutions 246Recommended Reading 249
Chapter 8: Numerical Simulation 2518.1 Introduction 2518.2 Molecular Dynamics 2538.3 Random Sequences 2598.4 Monte Carlo Method 2618.5 Umbrella Sampling 2728.6 Discussion 274Recommended Reading 275
Chapter 9: Dynamics 2779.1 Brownian Motion 2779.2 Fractal Properties of Brownian Trajectories 2829.3 Smoluchowski Equation 2859.4 Diffusion Processes and the Fokker-Planck Equation 2889.5 Correlation Functions 2899.6 Kubo Formula and Sum Rules 2929.7 Generalized Brownian Motion 2939.8 Time Reversal 2969.9 Response Functions 2969.10 Fluctuation-Dissipation Theorem 2999.11 Onsager Reciprocity Relations 3019.12 Affinities and Fluxes 3039.13 Variational Principle 3069.14 An Application 308Recommended Reading 310
Chapter 10: Complex Systems 31110.1 Linear Polymers in Solution 31210.2 Percolation 32110.3 Disordered Systems 338Recommended Reading 356
Appendices 357Appendix A Legendre Transformation 359A.1 Legendre Transform 359A.2 Properties of the Legendre Transform 360A.3 Lagrange Multipliers 361
Appendix B Saddle Point Method 364B.1 Euler Integrals and the Saddle Point Method 364B.2 The Euler Gamma Function 366B.3 Properties of N-Dimensional Space 367B.4 Integral Representation of the Delta Function 368
Appendix C A Probability Refresher 369C.1 Events and Probability 369C.2 Random Variables 369C.3 Averages and Moments 370C.4 Conditional Probability: Independence 371C.5 Generating Function 372C.6 Central Limit Theorem 372C.7 Correlations 373
Appendix D Markov Chains 375D.1 Introduction 375D.2 Definitions 375D.3 Spectral Properties 376D.4 Ergodic Properties 377D.5 Convergence to Equilibrium 378Appendix E Fundamental Physical Constants 380
Bibliography 383Index 389