Statistical Mechanics in a Nutshell, Second Edition

Name: Statistical Mechanics in a Nutshell, Second Edition
Brand: Princeton University Press
Price: 78.49 EUR
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Luca Peliti(Autor*in)

Princeton University Press

2. Auflage

Erschienen am 6. August 2024

576 Seiten

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978-0-691-24845-5 (ISBN)

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Inhalt

Cover
Contents
List of Figures
List of Tables
Foreword
Preface to the Second Edition
Acknowledgments
1. Introduction
1.1 The Subject Matter of Statistical Mechanics
1.2 Statistical Postulates
1.3 An Example: The Ideal Gas
1.4 Conclusions
2. Thermodynamics
2.1 Thermodynamic Systems
2.2 Extensive Variables
2.3 The Central Problem of Thermodynamics
2.4 Entropy
2.5 Simple Problems
2.6 Heat and Work
2.7 Adiabatic Transformations and the Axiomatic Foundation of the Entropy Principle
2.8 The Fundamental Equation
2.9 Energy Scheme
2.10 Intensive Variables and Thermodynamic Potentials
2.11 Free Energy and Maxwell Relations
2.12 Gibbs Free Energy and Enthalpy
2.13 The Koenig-Born Diagram
2.14 Other Thermodynamic Potentials
2.15 The Measurement of the Chemical Potential
2.16 The Euler and Gibbs-Duhem Equations
2.17 Magnetic Systems
2.18 Equations of State
2.19 Stability
2.20 Chemical Reactions
2.21 Phase Coexistence
2.22 The Clausius-Clapeyron Equation
2.23 The Coexistence Curve
2.24 Coexistence of Several Phases
2.25 The Critical Point
2.26 Planar Interfaces
3. The Fundamental Postulate
3.1 Phase Space
3.2 Observables
3.3 The Fundamental Postulate: Entropy as Phase-Space Volume
3.4 Liouville's Theorem
3.5 Quantum States
3.6 Systems in Contact
3.7 Variational Principle
3.8 The Ideal Gas
3.9 The Probability Distribution
3.10 The Maxwell Distribution
3.11 The Ising Paramagnet
3.12 The Canonical Ensemble
3.13 Generalized Ensembles
3.14 The p-T Ensemble
3.15 Quantum Ensembles
3.16 The Grand Canonical Ensemble
3.17 The Gibbs Formula for the Entropy
3.18 Variational Derivation of the Ensembles
3.19 Fluctuations of Uncorrelated Particles
4. Interaction-Free Systems
4.1 Harmonic Oscillators
4.2 Photons and Phonons
4.3 Boson and Fermion Gases
4.4 Electrons in Metals
4.5 Relation between Pressure and Internal Energy
4.6 Diamagnetism
4.7 White Dwarfs
4.8 Variational Derivation of Fermi and Bose Statistics
4.9 Einstein Condensation
4.10 Adsorption
4.11 Internal Degrees of Freedom
4.12 Chemical Equilibria in Gases
5. Phase Transitions
5.1 Liquid-Gas Coexistence and Critical Point
5.2 Van der Waals Equation
5.3 Binary Mixtures
5.4 Lattice Gas
5.5 The Ising Model
5.6 Lee-Yang Theory of Phase Transitions
5.7 Symmetry Breaking
5.8 The Order Parameter
5.9 Peierls's Argument
5.10 The One-Dimensional Ising Model
5.11 Duality
5.12 Mean-Field Theory
5.13 Variational Principle
5.14 Correlation Functions
5.15 The Landau Theory
5.16 Critical Exponents
5.17 The Einstein Theory of Fluctuations
5.18 Ginzburg Criterion
5.19 Limit n8
5.20 Universality and Scaling
5.21 Partition Function of the Two-Dimensional Ising Model
6. Renormalization Group
6.1 Block Transformation
6.2 Decimation in the One-Dimensional Ising Model
6.3 Two-Dimensional Ising Model
6.4 Relevant and Irrelevant Operators
6.5 Finite Lattice Method
6.6 Renormalization in Fourier Space
6.7 Quadratic Anisotropy and Crossover
6.8 Critical Crossover
6.9 Cubic Anisotropy
6.10 Lower and Upper Critical Dimensions
6.11 Kosterlitz-Thouless Transition
7. Classical Fluids
7.1 The Partition Function of a Classical Fluid
7.2 Reduced Densities
7.3 The Density Functional Approach
7.4 Virial Expansion
7.5 Perturbation Theory
7.6 Liquid Solutions
7.7 Colloidal Suspensions
8. Numerical Simulation
8.1 Introduction
8.2 Molecular Dynamics
8.3 Thermostats in Molecular Dynamics
8.4 Monte Carlo Method
8.5 Umbrella Sampling
8.6 Accelerated Monte Carlo Methods
8.7 Discussion
9. Dynamics
9.1 Brownian Motion
9.2 Diffusion Coefficient and the Einstein Relation
9.3 Fractal Properties of Brownian Trajectories
9.4 Smoluchowski Equation
9.5 Diffusion Processes and the Fokker-Planck Equation
9.6 Correlation Functions
9.7 Kubo Formula and Sum Rules
9.8 Metastable States and Stochastic Resonance
9.9 Chemical Kinetics
9.10 Generalized Brownian Motion
9.11 Response Functions
9.12 Fluctuation-Dissipation Theorem
9.13 Onsager Reciprocity Relations
9.14 Affinities and Fluxes
9.15 Nonequilibrium Steady States
9.16 An Application
10. Stochastic Thermodynamics
10.1 Fundamentals
10.2 Thermodynamic Consistency and Stochastic Energetics
10.3 Stochastic Entropy
10.4 Simple Examples
10.5 Average Entropy Production Rate
10.6 Time Reversal
10.7 Fluctuation Relations
10.8 Adiabatic and Nonadiabatic Entropy Production
10.9 Thermodynamics of Information
10.10 Information Reservoirs
10.11 Copying Information
10.12 Uncertainty Relations
11. Complex Systems
11.1 Introduction
11.2 Linear Polymers in Solution
11.3 Percolation
11.4 Systems with Impurities
11.5 Spin Glasses
11.6 The Hopfield Model of Associative Memory
A. Probability Refresher
A.1 Events and Probability
A.2 Random Variables
A.3 Averages and Moments
A.4 Conditional Probability: Independence
A.5 Characteristic Functions
A.6 Central Limit Theorem
A.7 Correlations
A.8 Dirac's Delta "Function"
B. Convex Functions and the Legendre Transformation
B.1 Convex Functions
B.2 The Jensen Inequality
B.3 Legendre Transformation
B.4 Properties of the Legendre Transformation
B.5 Lagrange Multipliers
C. Partial and Functional Derivatives
C.1 Partial Derivatives
C.2 Functional Derivatives
D. Fourier Transforms
D.1 Fourier Series
D.2 Fourier Transform
D.3 Functions Defined on a Lattice: Brillouin Zones
D.4 Integral Representation of the Delta Function
E. Saddle-Point Integration
E.1 Euler Integrals and the Saddle-Point Method
E.2 The Euler Gamma Function
E.3 Properties of the N-Dimensional Space
F. Basics of Information Theory
F.1 Shannon Entropy
F.2 Mutual Information
G. Markov Chains
G.1 Definitions
G.2 Spectral Properties
G.3 Convergence to Stationarity
G.4 Non-ergodic Matrices
H. Fundamental Physical Constants
Bibliography
Author Index
Subject Index

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