This volume develops statistical descriptions of many-particle systems.
This volume develops statistical descriptions of many-particle systems. It connects microscopic models with macroscopic thermodynamic behavior.
Part I. Foundations
Chapter 1. Microstates and Macrostates
1.1 Configuration space 1.2 Phase space 1.3 Macroscopic observables 1.4 Counting states 1.5 Examples
Chapter 2. Probability in Physics
2.1 Ensembles 2.2 Statistical averages 2.3 Ergodic hypothesis (overview) 2.4 Fluctuations 2.5 Examples
Chapter 3. Entropy and Information
3.1 Statistical entropy 3.2 Boltzmann entropy 3.3 Gibbs entropy 3.4 Information-theoretic interpretation 3.5 Examples
Part II. Classical Statistical Mechanics
Chapter 4. Microcanonical Ensemble
4.1 Isolated systems 4.2 Energy constraints 4.3 Entropy maximization 4.4 Applications 4.5 Examples
Chapter 5. Canonical Ensemble
5.1 Systems in thermal equilibrium 5.2 Partition function 5.3 Thermodynamic quantities 4.4 Applications 5.5 Examples
Chapter 6. Grand Canonical Ensemble
6.1 Variable particle number 6.2 Chemical potential 6.3 Partition function 6.4 Applications 6.5 Examples
Part III. Quantum Statistical Mechanics
Chapter 7. Quantum Ensembles
7.1 Density operators 7.2 Quantum partition function 7.3 Applications 7.4 Examples 7.5 Connections
Chapter 8. Bose–Einstein Statistics
8.1 Bosons 8.2 Distribution functions 8.3 Condensation 8.4 Applications 8.5 Examples
Chapter 9. Fermi–Dirac Statistics
9.1 Fermions 9.2 Distribution functions 9.3 Degeneracy 9.4 Applications 9.5 Examples
Part IV. Phase Transitions
Chapter 10. Phase Transitions
10.1 Order parameters 10.2 First and second order transitions 10.3 Critical points 10.4 Applications 10.5 Examples
Chapter 11. Critical Phenomena
11.1 Scaling laws 11.2 Universality 11.3 Renormalization group (overview) 11.4 Applications 11.5 Examples
Chapter 12. Lattice Models
12.1 Ising model 12.2 Spin systems 12.3 Exact solutions (overview) 12.4 Applications 12.5 Examples
Part V. Kinetic Theory
Chapter 13. Boltzmann Equation
13.1 Distribution functions 13.2 Collision terms 13.3 Equilibrium solutions 13.4 Applications 13.5 Examples
Chapter 14. Transport Phenomena
14.1 Diffusion 14.2 Thermal conductivity 14.3 Viscosity 14.4 Applications 14.5 Examples
Chapter 15. Nonequilibrium Systems
15.1 Time evolution 15.2 Relaxation processes 15.3 Fluctuation-dissipation relations 15.4 Applications 15.5 Examples
Part VI. Structure of Matter
Chapter 16. Solids
16.1 Crystal structures 16.2 Lattice vibrations 16.3 Phonons 16.4 Applications 16.5 Examples
Chapter 17. Liquids and Gases
17.1 Equation of state 17.2 Intermolecular forces 17.3 Phase behavior 17.4 Applications 17.5 Examples
Chapter 18. Complex Systems
18.1 Polymers 18.2 Soft matter 18.3 Biological systems 18.4 Applications 18.5 Examples
Part VII. Applications
Chapter 19. Condensed Matter Physics
19.1 Electron systems 19.2 Magnetism 19.3 Superconductivity overview 19.4 Applications 19.5 Examples
Chapter 20. Chemical Physics
20.1 Reaction rates 20.2 Molecular distributions 20.3 Applications 20.4 Examples 20.5 Connections
Chapter 21. Computational Statistical Mechanics
21.1 Monte Carlo methods 21.2 Molecular dynamics 21.3 Simulation techniques 21.4 Applications 21.5 Examples
Part VIII. Research Directions
Chapter 22. Advanced Topics
22.1 Nonequilibrium statistical mechanics 22.2 Quantum many-body systems 22.3 Information theory links 22.4 Modern developments 22.5 Emerging areas
Chapter 23. Open Problems
23.1 Phase transition classification 23.2 Strongly correlated systems 23.3 Computational complexity 23.4 Multiscale modeling 23.5 Future directions
Chapter 24. Historical and Conceptual Notes
24.1 Development of statistical mechanics 24.2 Key contributors 24.3 Evolution of ensemble theory 24.4 Cross-disciplinary impact 24.5 Summary
Appendix
A. Partition function reference B. Distribution formulas C. Proof techniques checklist D. Simulation method tables E. Cross-reference to other MSC branches